diff --git a/include/mata/nfa/nfa.hh b/include/mata/nfa/nfa.hh
index c771052a5..59402ec69 100644
--- a/include/mata/nfa/nfa.hh
+++ b/include/mata/nfa/nfa.hh
@@ -669,12 +669,23 @@ Nfa complement(const Nfa& aut, const utils::OrdVector<Symbol>& symbols,
 /**
  * @brief Compute minimal deterministic automaton.
  *
- * @param[in] aut Automaton whose minimal version to compute.
+ * @param[in] aut NFA whose minimal version to compute.
  * @param[in] params Optional parameters to control the minimization algorithm:
- * - "algorithm": "brzozowski"
+ * - "algorithm": "brzozowski" (Default: "brzozowski")
  * @return Minimal deterministic automaton.
  */
-Nfa minimize(const Nfa &aut, const ParameterMap& params = { { "algorithm", "brzozowski" } });
+Nfa make_minimal_dfa(const Nfa &nfa, const ParameterMap& params = { { "algorithm", "brzozowski" } });
+
+/**
+ * @brief Compute minimal deterministic automaton.
+ *
+ * @param[in] aut DFA whose minimal version to compute. Trimming on the copy of the automaton
+ *  will be performed if the automaton is not already trimmed.
+ * @param[in] params Optional parameters to control the minimization algorithm:
+ * - "algorithm": "hopcroft", "brzozowski" (Default: "hopcroft")
+ * @return Minimal deterministic automaton.
+ */
+Nfa minimize(const Nfa &dfa, const ParameterMap& params = { { "algorithm", "hopcroft" } });
 
 /**
  * @brief Determinize automaton.
diff --git a/include/mata/nfa/plumbing.hh b/include/mata/nfa/plumbing.hh
index 9d1c08f0f..775affd6b 100644
--- a/include/mata/nfa/plumbing.hh
+++ b/include/mata/nfa/plumbing.hh
@@ -35,7 +35,9 @@ inline void complement(
                                        { "minimize",  "false"}}) { *result = complement(aut, alphabet, params);
 }
 
-inline void minimize(Nfa* res, const Nfa &aut) { *res = minimize(aut); }
+inline void minimize(Nfa* res, const Nfa &dfa, const ParameterMap& params = {{ "algorithm", "hopcroft" }}) { *res = minimize(dfa, params); }
+
+inline void make_minimal_dfa(Nfa* res, const Nfa &nfa, const ParameterMap& params = {{ "algorithm", "brzozowski" }}) { *res = make_minimal_dfa(nfa, params); }
 
 inline void determinize(Nfa* result, const Nfa& aut, std::unordered_map<StateSet, State> *subset_map = nullptr) {
     *result = determinize(aut, subset_map);
diff --git a/src/nfa/operations.cc b/src/nfa/operations.cc
index 21fe0caf7..ac6996a38 100644
--- a/src/nfa/operations.cc
+++ b/src/nfa/operations.cc
@@ -927,27 +927,54 @@ Nfa mata::nfa::algorithms::minimize_brzozowski(const Nfa& aut) {
     return determinize(revert(determinize(revert(aut))));
 }
 
-Nfa mata::nfa::minimize(
-                const Nfa& aut,
-                const ParameterMap& params)
-{
-    Nfa result;
-    // setting the default algorithm
-    decltype(algorithms::minimize_brzozowski)* algo = algorithms::minimize_brzozowski;
+Nfa mata::nfa::make_minimal_dfa(const Nfa& nfa, const ParameterMap& params) {
     if (!haskey(params, "algorithm")) {
         throw std::runtime_error(std::to_string(__func__) +
             " requires setting the \"algorithm\" key in the \"params\" argument; "
             "received: " + std::to_string(params));
     }
 
+    // Setting the algorithm. Default is Brzozowski.
     const std::string& str_algo = params.at("algorithm");
-    if ("brzozowski" == str_algo) {  /* default */ }
+    decltype(algorithms::minimize_brzozowski)* algo = algorithms::minimize_brzozowski;
+    if (str_algo == "brzozowski") { /* default */ }
     else {
+        throw std::runtime_error(std::string(__func__) +
+            " received an unknown value for the \"algorithm\" key: " + str_algo);
+    }
+
+    return algo(nfa);
+}
+
+Nfa mata::nfa::minimize(const Nfa &dfa, const ParameterMap& params)
+{
+    if (!haskey(params, "algorithm")) {
         throw std::runtime_error(std::to_string(__func__) +
-            " received an unknown value of the \"algorithm\" key: " + str_algo);
+            " requires setting the \"algorithm\" key in the \"params\" argument; "
+            "received: " + std::to_string(params));
     }
 
-    return algo(aut);
+    // Setting the algorithm. Default is Hopcroft.
+    const std::string& str_algo = params.at("algorithm");
+    decltype(algorithms::minimize_hopcroft)* algo = algorithms::minimize_hopcroft;
+    if (str_algo == "hopcroft") {
+        /* default */;
+    } else if (str_algo == "brzozowski") {
+        algo = algorithms::minimize_brzozowski;
+    } else {
+        throw std::runtime_error(std::string(__func__) +
+            " received an unknown value for the \"algorithm\" key: " + str_algo);
+    }
+
+    // Hopcroft algorithm does not work with non-trimmed automata.
+    if (str_algo == "hopcroft") {
+        const BoolVector is_used = dfa.get_useful_states();
+        bool is_trimmed = std::all_of(is_used.begin(), is_used.end(), [](bool b) { return b; });
+        if (!is_trimmed) {
+            return algo(Nfa(dfa).trim());
+        }
+    }
+    return algo(dfa);
 }
 
 // Anonymous namespace for the Hopcroft minimization algorithm.
@@ -1295,7 +1322,7 @@ Nfa mata::nfa::algorithms::minimize_hopcroft(const Nfa& dfa_trimmed) {
         for (const SymbolPost &symbol_post : dfa_trimmed.delta[q]) {
             assert(symbol_post.targets.size() == 1);
             const State target = brp.set_idx[*symbol_post.targets.begin()];
-            mut_state_post.push_back(SymbolPost{ symbol_post.symbol, StateSet{ target } });
+            mut_state_post.emplace_back(SymbolPost{ symbol_post.symbol, StateSet{ target } });
         }
     }
 
diff --git a/tests-integration/src/test-unary-op.cc b/tests-integration/src/test-unary-op.cc
index 770610d86..ece07a789 100644
--- a/tests-integration/src/test-unary-op.cc
+++ b/tests-integration/src/test-unary-op.cc
@@ -36,7 +36,7 @@ int main(int argc, char *argv[]) {
 
     // minimization test
     Nfa aut_min(aut);
-    aut_min = mata::nfa::minimize(aut_min);
+    aut_min = mata::nfa::make_minimal_dfa(aut_min);
     std::cout << "minimize:" << (mata::nfa::are_equivalent(aut, aut_min) ? "ok" : "fail") << std::endl;
 
     return EXIT_SUCCESS;
diff --git a/tests-integration/src/unary-operations.cc b/tests-integration/src/unary-operations.cc
index 9b2cb175f..f1c6a91e1 100644
--- a/tests-integration/src/unary-operations.cc
+++ b/tests-integration/src/unary-operations.cc
@@ -64,12 +64,12 @@ int main(int argc, char *argv[]) {
     TIME_END(reduce);
 
     Nfa minimized_aut;
-    TIME_BEGIN(minimize);
+    TIME_BEGIN(make_minimal_dfa);
     // > START OF PROFILED CODE
     // Only minimize and its callees will be measured
-    mata::nfa::plumbing::minimize(&minimized_aut, aut);
+    mata::nfa::plumbing::make_minimal_dfa(&minimized_aut, aut);
     // > END OF PROFILED CODE
-    TIME_END(minimize);
+    TIME_END(make_minimal_dfa);
 
     Nfa det_aut;
     TIME_BEGIN(determinize);
diff --git a/tests/nfa/nfa-plumbing.cc b/tests/nfa/nfa-plumbing.cc
index c85dc81cc..5d9c13a99 100644
--- a/tests/nfa/nfa-plumbing.cc
+++ b/tests/nfa/nfa-plumbing.cc
@@ -109,7 +109,7 @@ TEST_CASE("Mata::nfa::Plumbing") {
 
     SECTION("Mata::nfa::Plumbing::minimize") {
         FILL_WITH_AUT_A(lhs);
-        mata::nfa::plumbing::minimize(&result, lhs);
+        mata::nfa::plumbing::make_minimal_dfa(&result, lhs);
         CHECK(!result.is_lang_empty());
     }
 
diff --git a/tests/nfa/nfa.cc b/tests/nfa/nfa.cc
index 2213f4edb..0b13d8114 100644
--- a/tests/nfa/nfa.cc
+++ b/tests/nfa/nfa.cc
@@ -1017,7 +1017,7 @@ TEST_CASE("mata::nfa::minimize() for profiling", "[.profiling],[minimize]") {
     aut.delta.add(3, 110, 3);
     aut.delta.add(3, 111, 3);
     aut.delta.add(3, 114, 3);
-    minimize(&result, aut);
+    make_minimal_dfa(&result, aut);
 }
 
 TEST_CASE("mata::nfa::construct() correct calls")