diff --git a/libmamba/include/mamba/specs/match_spec.hpp b/libmamba/include/mamba/specs/match_spec.hpp
index a7269d162..8b3fa5784 100644
--- a/libmamba/include/mamba/specs/match_spec.hpp
+++ b/libmamba/include/mamba/specs/match_spec.hpp
@@ -14,6 +14,7 @@
 #include <unordered_map>
 
 #include "mamba/specs/channel_spec.hpp"
+#include "mamba/specs/version_spec.hpp"
 
 namespace mamba::specs
 {
@@ -37,8 +38,8 @@ namespace mamba::specs
         [[nodiscard]] auto name() const -> const std::string&;
         void set_name(std::string name);
 
-        [[nodiscard]] auto version() const -> const std::string&;
-        void set_version(std::string ver);
+        [[nodiscard]] auto version() const -> const VersionSpec&;
+        void set_version(VersionSpec ver);
 
         [[nodiscard]] auto build_number() const -> const std::string&;
         void set_build_number(std::string num);
@@ -67,9 +68,9 @@ namespace mamba::specs
     private:
 
         std::optional<ChannelSpec> m_channel;
+        VersionSpec m_version;
         std::string m_name_space;
         std::string m_name;
-        std::string m_version;
         std::string m_build_number;
         std::string m_build_string;
         // TODO can put inside channel spec
diff --git a/libmamba/include/mamba/specs/version_spec.hpp b/libmamba/include/mamba/specs/version_spec.hpp
index c37c36ff2..b5dbc9c9d 100644
--- a/libmamba/include/mamba/specs/version_spec.hpp
+++ b/libmamba/include/mamba/specs/version_spec.hpp
@@ -48,6 +48,13 @@ namespace mamba::specs
 
         [[nodiscard]] auto str() const -> std::string;
 
+        /**
+         * An alternative string representation of the version spec.
+         *
+         * Attempts to be compatible with conda-build/libsolv.
+         */
+        [[nodiscard]] auto str_conda_build() const -> std::string;
+
     private:
 
         struct free_interval
@@ -148,6 +155,15 @@ namespace mamba::specs
         VersionSpec() = default;
         explicit VersionSpec(tree_type&& tree) noexcept;
 
+        /**
+         * Returns wether the VersionSpec is unconstrained.
+         *
+         * Due to the complex nature of VersionSpec expressions, it is not always easy to know
+         * whether a complex expression can be simpified to the unconstrained one.
+         * This functions only handles the trivial cases.
+         */
+        [[nodiscard]] auto is_explicitly_free() const -> bool;
+
         /**
          * A string representation of the version spec.
          *
@@ -156,6 +172,13 @@ namespace mamba::specs
          */
         [[nodiscard]] auto str() const -> std::string;
 
+        /**
+         * An alternative string representation of the version spec.
+         *
+         * Attempts to be compatible with conda-build/libsolv.
+         */
+        [[nodiscard]] auto str_conda_build() const -> std::string;
+
         /**
          * True if the set described by the VersionSpec contains the given version.
          */
@@ -177,6 +200,11 @@ namespace mamba::specs
 template <>
 struct fmt::formatter<mamba::specs::VersionPredicate>
 {
+    /**
+     * Change the representation of some predicates not understood by conda-build/libsolv.
+     */
+    bool conda_build_form = false;
+
     auto parse(format_parse_context& ctx) -> decltype(ctx.begin());
 
     auto format(const ::mamba::specs::VersionPredicate& pred, format_context& ctx)
@@ -186,6 +214,11 @@ struct fmt::formatter<mamba::specs::VersionPredicate>
 template <>
 struct fmt::formatter<mamba::specs::VersionSpec>
 {
+    /**
+     * Change the representation of some predicates not understood by conda-build/libsolv.
+     */
+    bool conda_build_form = false;
+
     auto parse(format_parse_context& ctx) -> decltype(ctx.begin());
 
     auto format(const ::mamba::specs::VersionSpec& spec, format_context& ctx) -> decltype(ctx.out());
diff --git a/libmamba/src/api/install.cpp b/libmamba/src/api/install.cpp
index e3ca06ea8..59d32d649 100644
--- a/libmamba/src/api/install.cpp
+++ b/libmamba/src/api/install.cpp
@@ -358,7 +358,7 @@ namespace mamba
                 PackageInfo p(ms.name());
                 p.url = ms.url();
                 p.build_string = ms.build_string();
-                p.version = ms.version();
+                p.version = ms.version().str();
                 if (ms.channel().has_value())
                 {
                     p.channel = ms.channel()->location();
diff --git a/libmamba/src/core/satisfiability_error.cpp b/libmamba/src/core/satisfiability_error.cpp
index a815b4ed6..67379d116 100644
--- a/libmamba/src/core/satisfiability_error.cpp
+++ b/libmamba/src/core/satisfiability_error.cpp
@@ -148,7 +148,7 @@ namespace mamba
 
             std::vector<old_node_id_list> groups{};
 
-            std::size_t const n_nodes = node_indices.size();
+            const std::size_t n_nodes = node_indices.size();
             std::vector<bool> node_added_to_a_group(n_nodes, false);
             for (std::size_t i = 0; i < n_nodes; ++i)
             {
@@ -538,14 +538,45 @@ namespace mamba
      *  Implementation of CompressedProblemsGraph::RoughCompare  *
      *************************************************************/
 
+    namespace
+    {
+        template <typename T>
+        auto invoke_name(T&& e) -> decltype(auto)
+        {
+            using TT = std::remove_cv_t<std::remove_reference_t<T>>;
+            return std::invoke(&TT::name, std::forward<T>(e));
+        }
+
+        template <typename T>
+        auto invoke_version(T&& e) -> decltype(auto)
+        {
+            using TT = std::remove_cv_t<std::remove_reference_t<T>>;
+            using Ver = decltype(std::invoke(&TT::version, std::forward<T>(e)));
+            Ver v = std::invoke(&TT::version, std::forward<T>(e));
+            if constexpr (std::is_same_v<std::decay_t<decltype(v)>, specs::VersionSpec>)
+            {
+                return std::forward<Ver>(v).str();
+            }
+            else
+            {
+                return v;
+            }
+        }
+    }
+
     template <typename T>
-    bool CompressedProblemsGraph::RoughCompare<T>::operator()(const T& a, const T& b) const
+    auto CompressedProblemsGraph::RoughCompare<T>::operator()(const T& a, const T& b) const -> bool
     {
         auto attrs = [](const auto& x)
         {
-            return std::tie(
-                std::invoke(&T::name, x),
-                std::invoke(&T::version, x),
+            using Attrs = std::tuple<
+                decltype(invoke_name(x)),
+                decltype(invoke_version(x)),
+                decltype(std::invoke(&T::build_number, x)),
+                decltype(std::invoke(&T::build_string, x))>;
+            return Attrs(
+                invoke_name(x),
+                invoke_version(x),
                 std::invoke(&T::build_number, x),
                 std::invoke(&T::build_string, x)
             );
@@ -562,16 +593,6 @@ namespace mamba
      *  Implementation of CompressedProblemsGraph::NamedList  *
      **********************************************************/
 
-    namespace
-    {
-        template <typename T>
-        decltype(auto) invoke_name(T&& e)
-        {
-            using TT = std::remove_cv_t<std::remove_reference_t<T>>;
-            return std::invoke(&TT::name, std::forward<T>(e));
-        }
-    }
-
     template <typename T, typename A>
     template <typename InputIterator>
     CompressedProblemsGraph::NamedList<T, A>::NamedList(InputIterator first, InputIterator last)
@@ -650,13 +671,13 @@ namespace mamba
     ) const -> std::pair<std::string, std::size_t>
     {
         auto versions = std::vector<std::string>(size());
-        auto invoke_version = [](auto&& v) -> decltype(auto)
-        {
-            using TT = std::remove_cv_t<std::remove_reference_t<decltype(v)>>;
-            return std::invoke(&TT::version, std::forward<decltype(v)>(v));
-        };
         // TODO(C++20) *this | std::ranges::transform(invoke_version) | ranges::unique
-        std::transform(begin(), end(), versions.begin(), invoke_version);
+        std::transform(
+            begin(),
+            end(),
+            versions.begin(),
+            [](const auto& x) { return invoke_version(x); }
+        );
         if (remove_duplicates)
         {
             versions.erase(std::unique(versions.begin(), versions.end()), versions.end());
@@ -1036,7 +1057,7 @@ namespace mamba
 
             const TreeNodeIter children_begin = out;
             // TODO(C++20) an enumerate view ``views::zip(views::iota(), children_ids)``
-            std::size_t const n_children = children_ids.size();
+            const std::size_t n_children = children_ids.size();
             for (std::size_t i = 0; i < n_children; ++i)
             {
                 const bool last = (i == n_children - 1);
@@ -1228,7 +1249,7 @@ namespace mamba
 
         void TreeExplainer::write_ancestry(const std::vector<SiblingNumber>& ancestry)
         {
-            std::size_t const size = ancestry.size();
+            const std::size_t size = ancestry.size();
             const auto indents = m_format.indents;
             if (size > 0)
             {
@@ -1434,7 +1455,7 @@ namespace mamba
 
         void TreeExplainer::write_path(const std::vector<TreeNode>& path)
         {
-            std::size_t const length = path.size();
+            const std::size_t length = path.size();
             for (std::size_t i = 0; i < length; ++i)
             {
                 const bool last = (i == length - 1);
diff --git a/libmamba/src/core/solver.cpp b/libmamba/src/core/solver.cpp
index 1b83247e8..7092a8693 100644
--- a/libmamba/src/core/solver.cpp
+++ b/libmamba/src/core/solver.cpp
@@ -96,7 +96,8 @@ namespace mamba
             return m_jobs->push_back(job_flag | SOLVER_SOLVABLE_PROVIDES, m_pool.matchspec2id(ms));
         }
 
-        if (ms.channel().has_value() || !ms.version().empty() || !ms.build_string().empty())
+        if (ms.channel().has_value() || !ms.version().is_explicitly_free()
+            || !ms.build_string().empty())
         {
             Console::stream() << ms.conda_build_form()
                               << ": overriding channel, version and build from "
@@ -105,7 +106,7 @@ namespace mamba
 
         auto ms_modified = ms;
         ms_modified.set_channel(specs::ChannelSpec::parse(solvable->channel()));
-        ms_modified.set_version(std::string(solvable->version()));
+        ms_modified.set_version(specs::VersionSpec::parse(solvable->version()));
         ms_modified.set_build_string(std::string(solvable->build_string()));
 
         LOG_INFO << "Reinstall " << ms_modified.conda_build_form() << " from channel "
diff --git a/libmamba/src/core/transaction.cpp b/libmamba/src/core/transaction.cpp
index 65d426607..a096b0d05 100644
--- a/libmamba/src/core/transaction.cpp
+++ b/libmamba/src/core/transaction.cpp
@@ -73,7 +73,7 @@ namespace mamba
                 auto& p = out.back();
                 p.url = ms.url();
                 p.build_string = ms.build_string();
-                p.version = ms.version();
+                p.version = ms.version().str_conda_build();
                 if (ms.channel().has_value())
                 {
                     p.channel = ms.channel()->location();
diff --git a/libmamba/src/specs/match_spec.cpp b/libmamba/src/specs/match_spec.cpp
index a86657142..2cf0220b1 100644
--- a/libmamba/src/specs/match_spec.cpp
+++ b/libmamba/src/specs/match_spec.cpp
@@ -77,7 +77,7 @@ namespace mamba::specs
 
         // Version
         std::tie(head, tail) = util::rsplit_once(head.value(), '-');
-        out.m_version = tail;
+        out.m_version = VersionSpec::parse(tail);
         if (!head.has_value())
         {
             fail_parse();
@@ -192,12 +192,14 @@ namespace mamba::specs
             spec_str.push_back('*');
         }
         // This is #6 of the spec parsing
+        // Look for version *and* build string and separator
+        auto version_and_build = std::string();
         static std::regex version_build_re("([^ =<>!~]+)?([><!=~ ].+)?");
         std::smatch vb_match;
         if (std::regex_match(spec_str, vb_match, version_build_re))
         {
             out.m_name = vb_match[1].str();
-            out.m_version = util::strip(vb_match[2].str());
+            version_and_build = util::strip(vb_match[2].str());
             if (out.m_name.size() == 0)
             {
                 throw std::runtime_error("Invalid spec, no package name found: " + spec_str);
@@ -210,9 +212,9 @@ namespace mamba::specs
 
         // # Step 7. otherwise sort out version + build
         // spec_str = spec_str and spec_str.strip()
-        if (!out.m_version.empty())
+        if (!version_and_build.empty())
         {
-            if (out.m_version.find('[') != out.m_version.npos)
+            if (version_and_build.find('[') != std::string::npos)
             {
                 throw std::runtime_error(util::concat(
                     R"(Invalid match spec: multiple bracket sections not allowed ")",
@@ -221,38 +223,15 @@ namespace mamba::specs
                 ));
             }
 
-            out.m_version = std::string(util::strip(out.m_version));
-            auto [pv, pb] = parse_version_and_build(std::string(util::strip(out.m_version)));
+            auto [pv, pb] = parse_version_and_build(version_and_build);
 
-            out.m_version = pv;
+            out.m_version = VersionSpec::parse(pv);
             out.m_build_string = pb;
-
-            // translate version '=1.2.3' to '1.2.3*'
-            // is it a simple version starting with '='? i.e. '=1.2.3'
-            if (out.m_version.size() >= 2 && out.m_version[0] == '=')
-            {
-                auto rest = out.m_version.substr(1);
-                if (out.m_version[1] == '=' && out.m_build_string.empty())
-                {
-                    out.m_version = out.m_version.substr(2);
-                }
-                else if (rest.find_first_of("=,|") == rest.npos)
-                {
-                    if (out.m_build_string.empty() && out.m_version.back() != '*')
-                    {
-                        out.m_version = util::concat(out.m_version, "*");
-                    }
-                    else
-                    {
-                        out.m_version = rest;
-                    }
-                }
-            }
         }
-        else
+        else  // no-op
         {
-            out.m_version = "";
-            out.m_build_string = "";
+            out.m_version = {};
+            out.m_build_string = {};
         }
 
         // TODO think about using a hash function here, (and elsewhere), like:
@@ -270,7 +249,7 @@ namespace mamba::specs
             }
             else if (k == "version")
             {
-                out.m_version = v;
+                out.m_version = VersionSpec::parse(v);
             }
             else if (k == "channel")
             {
@@ -351,12 +330,12 @@ namespace mamba::specs
         m_name = std::move(name);
     }
 
-    auto MatchSpec::version() const -> const std::string&
+    auto MatchSpec::version() const -> const VersionSpec&
     {
         return m_version;
     }
 
-    void MatchSpec::set_version(std::string ver)
+    void MatchSpec::set_version(VersionSpec ver)
     {
         m_version = std::move(ver);
     }
@@ -405,14 +384,17 @@ namespace mamba::specs
     {
         std::stringstream res;
         res << m_name;
-        if (!m_version.empty())
+        if (!m_version.is_explicitly_free())
         {
-            res << " " << m_version;
-            // if (!build.empty() && (build != "*"))
-            if (!m_build_string.empty())
-            {
-                res << " " << m_build_string;
-            }
+            res << " " << m_version.str_conda_build();
+        }
+        else if (!m_build_string.empty())
+        {
+            res << " *";
+        }
+        if (!m_build_string.empty())
+        {
+            res << " " << m_build_string;
         }
         return res.str();
     }
@@ -453,50 +435,16 @@ namespace mamba::specs
         auto is_complex_relation = [](const std::string& s)
         { return s.find_first_of("><$^|,") != s.npos; };
 
-        if (!m_version.empty())
+        if (!m_version.is_explicitly_free())
         {
-            if (is_complex_relation(m_version))
+            auto ver = m_version.str();
+            if (is_complex_relation(ver))  // TODO do on VersionSpec
             {
-                formatted_brackets.push_back(util::concat("version='", m_version, "'"));
-            }
-            else if (util::starts_with(m_version, "!=") || util::starts_with(m_version, "~="))
-            {
-                if (!m_build_string.empty())
-                {
-                    formatted_brackets.push_back(util::concat("version='", m_version, "'"));
-                }
-                else
-                {
-                    res << " " << m_version;
-                }
-            }
-            else if (util::ends_with(m_version, ".*"))
-            {
-                res << "=" + m_version.substr(0, m_version.size() - 2);
-            }
-            else if (m_version.back() == '*')
-            {
-                if (m_version.size() == 1)
-                {
-                    res << "=*";
-                }
-                else if (util::starts_with(m_version, "="))
-                {
-                    res << m_version.substr(0, m_version.size() - 1);
-                }
-                else
-                {
-                    res << "=" + m_version.substr(0, m_version.size() - 1);
-                }
-            }
-            else if (util::starts_with(m_version, "=="))
-            {
-                res << m_version;
-                version_exact = true;
+                formatted_brackets.push_back(util::concat("version='", ver, "'"));
             }
             else
             {
-                res << "==" << m_version;
+                res << ver;
                 version_exact = true;
             }
         }
@@ -566,7 +514,7 @@ namespace mamba::specs
 
     auto MatchSpec::is_simple() const -> bool
     {
-        return m_version.empty() && m_build_string.empty() && m_build_number.empty();
+        return m_version.is_explicitly_free() && m_build_string.empty() && m_build_number.empty();
     }
 
     auto MatchSpec::is_file() const -> bool
diff --git a/libmamba/src/specs/version_spec.cpp b/libmamba/src/specs/version_spec.cpp
index 85ebd99e4..d395e7a35 100644
--- a/libmamba/src/specs/version_spec.cpp
+++ b/libmamba/src/specs/version_spec.cpp
@@ -160,6 +160,11 @@ namespace mamba::specs
         return fmt::format("{}", *this);
     }
 
+    auto VersionPredicate::str_conda_build() const -> std::string
+    {
+        return fmt::format("{:b}", *this);
+    }
+
     VersionPredicate::VersionPredicate(Version ver, BinaryOperator op)
         : m_version(std::move(ver))
         , m_operator(std::move(op))
@@ -181,10 +186,10 @@ auto
 fmt::formatter<mamba::specs::VersionPredicate>::parse(format_parse_context& ctx)
     -> decltype(ctx.begin())
 {
-    // make sure that range is empty
-    if (ctx.begin() != ctx.end() && *ctx.begin() != '}')
+    if (auto it = std::find(ctx.begin(), ctx.end(), 'b'); it < ctx.end())
     {
-        throw fmt::format_error("Invalid format");
+        conda_build_form = true;
+        return ++it;
     }
     return ctx.begin();
 }
@@ -239,7 +244,14 @@ fmt::formatter<mamba::specs::VersionPredicate>::format(
             }
             if constexpr (std::is_same_v<Op, VersionPredicate::starts_with>)
             {
-                out = fmt::format_to(out, "{}{}", VersionSpec::starts_with_str, pred.m_version);
+                if (conda_build_form)
+                {
+                    out = fmt::format_to(out, "{}{}", pred.m_version, VersionSpec::glob_suffix_str);
+                }
+                else
+                {
+                    out = fmt::format_to(out, "{}{}", VersionSpec::starts_with_str, pred.m_version);
+                }
             }
             if constexpr (std::is_same_v<Op, VersionPredicate::not_starts_with>)
             {
@@ -283,11 +295,23 @@ namespace mamba::specs
         return m_tree.evaluate([&point](const auto& node) { return node.contains(point); });
     }
 
+    auto VersionSpec::is_explicitly_free() const -> bool
+    {
+        const auto free_pred = VersionPredicate::make_free();
+        const auto is_free_pred = [&free_pred](const auto& node) { return node == free_pred; };
+        return m_tree.empty() || ((m_tree.size() == 1) && m_tree.evaluate(is_free_pred));
+    }
+
     auto VersionSpec::str() const -> std::string
     {
         return fmt::format("{}", *this);
     }
 
+    auto VersionSpec::str_conda_build() const -> std::string
+    {
+        return fmt::format("{:b}", *this);
+    }
+
     namespace
     {
         template <typename Val, typename Range>
@@ -464,10 +488,10 @@ namespace mamba::specs
 auto
 fmt::formatter<mamba::specs::VersionSpec>::parse(format_parse_context& ctx) -> decltype(ctx.begin())
 {
-    // make sure that range is empty
-    if (ctx.begin() != ctx.end() && *ctx.begin() != '}')
+    if (auto it = std::find(ctx.begin(), ctx.end(), 'b'); it < ctx.end())
     {
-        throw fmt::format_error("Invalid format");
+        conda_build_form = true;
+        return ++it;
     }
     return ctx.begin();
 }
@@ -511,7 +535,7 @@ fmt::formatter<mamba::specs::VersionSpec>::format(
             }
             if constexpr (std::is_same_v<Token, tree_type::variable_type>)
             {
-                out = fmt::format_to(out, "{}", token);
+                out = fmt::format_to(out, conda_build_form ? "{:b}" : "{}", token);
             }
         }
     );
diff --git a/libmamba/tests/src/specs/test_match_spec.cpp b/libmamba/tests/src/specs/test_match_spec.cpp
index 02a3dc73c..f46cfed07 100644
--- a/libmamba/tests/src/specs/test_match_spec.cpp
+++ b/libmamba/tests/src/specs/test_match_spec.cpp
@@ -67,29 +67,29 @@ TEST_SUITE("specs::match_spec")
     {
         {
             auto ms = MatchSpec::parse("xtensor==0.12.3");
-            CHECK_EQ(ms.version(), "0.12.3");
+            CHECK_EQ(ms.version().str(), "==0.12.3");
             CHECK_EQ(ms.name(), "xtensor");
         }
         {
             auto ms = MatchSpec::parse("");
-            CHECK_EQ(ms.version(), "");
+            CHECK_EQ(ms.version().str(), "=*");
             CHECK_EQ(ms.name(), "");
         }
         {
             auto ms = MatchSpec::parse("ipykernel");
-            CHECK_EQ(ms.version(), "");
+            CHECK_EQ(ms.version().str(), "=*");
             CHECK_EQ(ms.name(), "ipykernel");
         }
         {
             auto ms = MatchSpec::parse("ipykernel ");
-            CHECK_EQ(ms.version(), "");
+            CHECK_EQ(ms.version().str(), "=*");
             CHECK_EQ(ms.name(), "ipykernel");
         }
         {
             auto ms = MatchSpec::parse("numpy 1.7*");
-            CHECK_EQ(ms.version(), "1.7*");
+            CHECK_EQ(ms.version().str(), "=1.7");
             CHECK_EQ(ms.name(), "numpy");
-            CHECK_EQ(ms.conda_build_form(), "numpy 1.7*");
+            CHECK_EQ(ms.conda_build_form(), "numpy 1.7.*");
             CHECK_EQ(ms.str(), "numpy=1.7");
         }
         {
@@ -98,11 +98,11 @@ TEST_SUITE("specs::match_spec")
             // CHECK_EQ(ms.version, "1.7|1.8");
             CHECK_EQ(ms.name(), "numpy");
             CHECK_EQ(ms.brackets["version"], "1.7|1.8");
-            CHECK_EQ(ms.str(), "numpy[version='1.7|1.8']");
+            CHECK_EQ(ms.str(), "numpy[version='==1.7|==1.8']");
         }
         {
             auto ms = MatchSpec::parse("conda-forge/linux-64::xtensor==0.12.3");
-            CHECK_EQ(ms.version(), "0.12.3");
+            CHECK_EQ(ms.version().str(), "==0.12.3");
             CHECK_EQ(ms.name(), "xtensor");
             REQUIRE(ms.channel().has_value());
             CHECK_EQ(ms.channel()->location(), "conda-forge");
@@ -111,7 +111,7 @@ TEST_SUITE("specs::match_spec")
         }
         {
             auto ms = MatchSpec::parse("conda-forge::foo[build=3](target=blarg,optional)");
-            CHECK_EQ(ms.version(), "");
+            CHECK_EQ(ms.version().str(), "=*");
             CHECK_EQ(ms.name(), "foo");
             REQUIRE(ms.channel().has_value());
             CHECK_EQ(ms.channel()->location(), "conda-forge");
@@ -136,7 +136,7 @@ TEST_SUITE("specs::match_spec")
                 "https://conda.anaconda.org/conda-forge/linux-64/_libgcc_mutex-0.1-conda_forge.tar.bz2"
             );
             CHECK_EQ(ms.name(), "_libgcc_mutex");
-            CHECK_EQ(ms.version(), "0.1");
+            CHECK_EQ(ms.version().str(), "==0.1");
             CHECK_EQ(ms.build_string(), "conda_forge");
             CHECK_EQ(
                 ms.url(),
@@ -149,7 +149,7 @@ TEST_SUITE("specs::match_spec")
                 "https://conda.anaconda.org/conda-forge/linux-64/libgcc-ng-11.2.0-h1d223b6_13.tar.bz2"
             );
             CHECK_EQ(ms.name(), "libgcc-ng");
-            CHECK_EQ(ms.version(), "11.2.0");
+            CHECK_EQ(ms.version().str(), "==11.2.0");
             CHECK_EQ(ms.build_string(), "h1d223b6_13");
             CHECK_EQ(
                 ms.url(),
@@ -162,7 +162,7 @@ TEST_SUITE("specs::match_spec")
                 "/home/randomguy/Downloads/linux-64/_libgcc_mutex-0.1-conda_forge.tar.bz2"
             );
             CHECK_EQ(ms.name(), "_libgcc_mutex");
-            CHECK_EQ(ms.version(), "0.1");
+            CHECK_EQ(ms.version().str(), "==0.1");
             CHECK_EQ(ms.build_string(), "conda_forge");
             if (util::on_win)
             {
@@ -199,21 +199,21 @@ TEST_SUITE("specs::match_spec")
         }
         {
             auto ms = MatchSpec::parse("foo=1.0=2");
-            CHECK_EQ(ms.conda_build_form(), "foo 1.0 2");
-            CHECK_EQ(ms.str(), "foo==1.0=2");
+            CHECK_EQ(ms.conda_build_form(), "foo 1.0.* 2");
+            CHECK_EQ(ms.str(), "foo=1.0=2");
         }
         {
             auto ms = MatchSpec::parse("foo=1.0=2[md5=123123123, license=BSD-3, fn='test 123.tar.bz2']"
             );
-            CHECK_EQ(ms.conda_build_form(), "foo 1.0 2");
-            CHECK_EQ(ms.str(), "foo==1.0=2[md5=123123123,license=BSD-3,fn='test 123.tar.bz2']");
+            CHECK_EQ(ms.conda_build_form(), "foo 1.0.* 2");
+            CHECK_EQ(ms.str(), "foo=1.0=2[md5=123123123,license=BSD-3,fn='test 123.tar.bz2']");
         }
         {
             auto ms = MatchSpec::parse(
                 "foo=1.0=2[md5=123123123, license=BSD-3, fn='test 123.tar.bz2', url='abcdef']"
             );
-            CHECK_EQ(ms.conda_build_form(), "foo 1.0 2");
-            CHECK_EQ(ms.str(), "foo==1.0=2[url=abcdef,md5=123123123,license=BSD-3]");
+            CHECK_EQ(ms.conda_build_form(), "foo 1.0.* 2");
+            CHECK_EQ(ms.str(), "foo=1.0=2[url=abcdef,md5=123123123,license=BSD-3]");
         }
         {
             auto ms = MatchSpec::parse("libblas=*=*mkl");
@@ -222,12 +222,14 @@ TEST_SUITE("specs::match_spec")
         }
         {
             auto ms = MatchSpec::parse("libblas=0.15*");
-            CHECK_EQ(ms.conda_build_form(), "libblas 0.15*");
+            CHECK_EQ(ms.conda_build_form(), "libblas 0.15*.*");
         }
         {
+            // '*' is part of the version, not the glob
             auto ms = MatchSpec::parse("xtensor =0.15*");
-            CHECK_EQ(ms.conda_build_form(), "xtensor 0.15*");
-            CHECK_EQ(ms.str(), "xtensor=0.15");
+            CHECK_EQ(ms.conda_build_form(), "xtensor 0.15*.*");
+            CHECK_EQ(ms.str(), "xtensor=0.15*");
+            CHECK_EQ(ms.version().str(), "=0.15*");
         }
         {
             auto ms = MatchSpec::parse("numpy=1.20");
diff --git a/libmamba/tests/src/specs/test_version_spec.cpp b/libmamba/tests/src/specs/test_version_spec.cpp
index a68a7abd2..c1bb437d6 100644
--- a/libmamba/tests/src/specs/test_version_spec.cpp
+++ b/libmamba/tests/src/specs/test_version_spec.cpp
@@ -80,6 +80,7 @@ TEST_SUITE("specs::version_spec")
         CHECK_FALSE(sw.contains(v3));
         CHECK_FALSE(sw.contains(v4));
         CHECK_EQ(sw.str(), "=2.0");
+        CHECK_EQ(sw.str_conda_build(), "2.0.*");
 
         const auto nsw = VersionPredicate::make_not_starts_with(v2);
         CHECK(nsw.contains(v1));
@@ -397,4 +398,42 @@ TEST_SUITE("specs::version_spec")
             }
         }
     }
+
+    TEST_CASE("VersionSpec::str")
+    {
+        SUBCASE("2.3")
+        {
+            auto vs = VersionSpec::parse("2.3");
+            CHECK_EQ(vs.str(), "==2.3");
+            CHECK_EQ(vs.str_conda_build(), "==2.3");
+        }
+
+        SUBCASE("=2.3,<3.0")
+        {
+            auto vs = VersionSpec::parse("=2.3,<3.0");
+            CHECK_EQ(vs.str(), "=2.3,<3.0");
+            CHECK_EQ(vs.str_conda_build(), "2.3.*,<3.0");
+        }
+    }
+
+    TEST_CASE("VersionSpec::is_free")
+    {
+        {
+            using namespace mamba::util;
+
+            auto parser = InfixParser<VersionPredicate, BoolOperator>{};
+            parser.push_variable(VersionPredicate::make_free());
+            parser.finalize();
+            auto spec = VersionSpec(std::move(parser).tree());
+
+            CHECK(spec.is_explicitly_free());
+        }
+
+        CHECK(VersionSpec().is_explicitly_free());
+        CHECK(VersionSpec::parse("*").is_explicitly_free());
+        CHECK(VersionSpec::parse("").is_explicitly_free());
+
+        CHECK_FALSE(VersionSpec::parse("==2.3|!=2.3").is_explicitly_free());
+        CHECK_FALSE(VersionSpec::parse("=2.3,<3.0").is_explicitly_free());
+    }
 }
diff --git a/libmambapy/tests/test_specs.py b/libmambapy/tests/test_specs.py
index ab6e80b73..fb81fb809 100644
--- a/libmambapy/tests/test_specs.py
+++ b/libmambapy/tests/test_specs.py
@@ -666,4 +666,4 @@ def test_MatchSpec():
     ms = MatchSpec.parse("conda-forge::python=3.7=*pypy")
 
     # str
-    assert str(ms) == "conda-forge::python==3.7[build=*pypy]"
+    assert str(ms) == "conda-forge::python=3.7[build=*pypy]"