diff --git a/src/analysis_and_optimization/Dataflow_utils.ml b/src/analysis_and_optimization/Dataflow_utils.ml
index 59a6b4147d..bb2062fc7a 100644
--- a/src/analysis_and_optimization/Dataflow_utils.ml
+++ b/src/analysis_and_optimization/Dataflow_utils.ml
@@ -174,7 +174,7 @@ let build_cf_graphs ?(flatten_loops = false) ?(blocks_after_body = true)
                   Set.Poly.diff substmt_state_unlooped.breaks in_state.breaks ]
           in
           ({substmt_state_unlooped with exits= loop_exits}, loop_predecessors)
-      | Block _ when blocks_after_body ->
+      | (Block _ | Profile _) when blocks_after_body ->
           (* Block statements are preceded by the natural exit points of the block
              body *)
           let block_predecessors = substmt_state_unlooped.exits in
diff --git a/src/analysis_and_optimization/Mir_utils.ml b/src/analysis_and_optimization/Mir_utils.ml
index 28d9b54aec..5c098ce1eb 100644
--- a/src/analysis_and_optimization/Mir_utils.ml
+++ b/src/analysis_and_optimization/Mir_utils.ml
@@ -109,7 +109,7 @@ let rec var_declarations Stmt.Fixed.{pattern; _} : string Set.Poly.t =
   | IfElse (_, s, None) | While (_, s) | For {body= s; _} -> var_declarations s
   | IfElse (_, s1, Some s2) ->
       Set.Poly.union (var_declarations s1) (var_declarations s2)
-  | Block slist | SList slist ->
+  | Block slist | SList slist | Profile (_, slist) ->
       Set.Poly.union_list (List.map ~f:var_declarations slist)
   | _ -> Set.Poly.empty
 
@@ -431,6 +431,7 @@ let cleanup_empty_stmts stmts =
   let is_decl = function {pattern= Decl _; _} -> true | _ -> false in
   let flatten_block s =
     match s.pattern with
+    (* NB: Does not include Profile since we don't want to remove those blocks *)
     | SList ls | Block ls ->
         if List.for_all ~f:(Fn.non is_decl) ls then ls else [s]
     | _ -> [s] in
diff --git a/src/middle/Stmt.ml b/src/middle/Stmt.ml
index fa33ca2761..4b2c94e605 100644
--- a/src/middle/Stmt.ml
+++ b/src/middle/Stmt.ml
@@ -51,8 +51,10 @@ module Fixed = struct
       | For {loopvar; lower; upper; body} ->
           Fmt.pf ppf "for(%s in %a:%a) %a" loopvar pp_e lower pp_e upper pp_s
             body
-      | Profile (_, stmts) ->
-          Fmt.pf ppf "{@;<1 2>@[<v>%a@]@;}" Fmt.(list pp_s ~sep:cut) stmts
+      | Profile (name, stmts) ->
+          Fmt.pf ppf "profile(%s){@;<1 2>@[<v>%a@]@;}" name
+            Fmt.(list pp_s ~sep:cut)
+            stmts
       | Block stmts ->
           Fmt.pf ppf "{@;<1 2>@[<v>%a@]@;}" Fmt.(list pp_s ~sep:cut) stmts
       | SList stmts -> Fmt.(list pp_s ~sep:cut |> vbox) ppf stmts
diff --git a/test/integration/good/compiler-optimizations/cpp.expected b/test/integration/good/compiler-optimizations/cpp.expected
index ac6f345221..d54d6644e0 100644
--- a/test/integration/good/compiler-optimizations/cpp.expected
+++ b/test/integration/good/compiler-optimizations/cpp.expected
@@ -4172,18 +4172,21 @@ namespace copy_prop_profile_model_namespace {
 using stan::model::model_base_crtp;
 using namespace stan::math;
 stan::math::profile_map profiles__;
-static constexpr std::array<const char*, 16> locations_array__ =
+static constexpr std::array<const char*, 19> locations_array__ =
   {" (found before start of program)",
   " (in 'copy-prop-profile.stan', line 5, column 2 to column 16)",
   " (in 'copy-prop-profile.stan', line 9, column 13 to column 14)",
   " (in 'copy-prop-profile.stan', line 9, column 2 to column 20)",
   " (in 'copy-prop-profile.stan', line 12, column 15 to column 16)",
   " (in 'copy-prop-profile.stan', line 12, column 4 to column 45)",
+  " (in 'copy-prop-profile.stan', line 13, column 4 to column 15)",
   " (in 'copy-prop-profile.stan', line 11, column 2 to line 14, column 3)",
+  " (in 'copy-prop-profile.stan', line 16, column 2 to column 21)",
   " (in 'copy-prop-profile.stan', line 18, column 13 to column 14)",
   " (in 'copy-prop-profile.stan', line 18, column 2 to column 21)",
   " (in 'copy-prop-profile.stan', line 20, column 15 to column 16)",
   " (in 'copy-prop-profile.stan', line 20, column 4 to column 45)",
+  " (in 'copy-prop-profile.stan', line 21, column 4 to column 16)",
   " (in 'copy-prop-profile.stan', line 19, column 2 to line 22, column 3)",
   " (in 'copy-prop-profile.stan', line 24, column 2 to column 22)",
   " (in 'copy-prop-profile.stan', line 2, column 2 to column 17)",
@@ -4211,19 +4214,18 @@ class copy_prop_profile_model final : public model_base_crtp<copy_prop_profile_m
     // suppress unused var warning
     (void) DUMMY_VAR__;
     try {
-      int pos__;
-      pos__ = 1;
-      current_statement__ = 13;
+      int pos__ = std::numeric_limits<int>::min();
+      current_statement__ = 16;
       context__.validate_dims("data initialization", "N", "int",
         std::vector<size_t>{});
       N = std::numeric_limits<int>::min();
-      current_statement__ = 13;
+      current_statement__ = 16;
       N = context__.vals_i("N")[(1 - 1)];
-      current_statement__ = 13;
+      current_statement__ = 16;
       stan::math::check_greater_or_equal(function__, "N", N, 0);
-      current_statement__ = 14;
+      current_statement__ = 17;
       stan::math::validate_non_negative_index("X", "N", N);
-      current_statement__ = 15;
+      current_statement__ = 18;
       stan::math::validate_non_negative_index("X", "N", N);
     } catch (const std::exception& e) {
       stan::lang::rethrow_located(e, locations_array__[current_statement__]);
@@ -4257,18 +4259,22 @@ class copy_prop_profile_model final : public model_base_crtp<copy_prop_profile_m
     // suppress unused var warning
     (void) function__;
     try {
-      local_scalar_t__ lcm_sym5__;
-      Eigen::Matrix<local_scalar_t__,1,-1> lcm_sym4__;
-      Eigen::Matrix<local_scalar_t__,-1,-1> X;
+      double lcm_sym6__;
+      double lcm_sym5__;
+      Eigen::Matrix<double,1,-1> lcm_sym4__;
+      stan::conditional_var_value_t<local_scalar_t__,
+        Eigen::Matrix<local_scalar_t__,-1,-1>> X;
       current_statement__ = 1;
-      X = in__.template read<Eigen::Matrix<local_scalar_t__,-1,-1>>(N, N);
+      X = in__.template read<
+            stan::conditional_var_value_t<local_scalar_t__,
+              Eigen::Matrix<local_scalar_t__,-1,-1>>>(N, N);
       {
         current_statement__ = 2;
         stan::math::validate_non_negative_index("vec", "N", N);
         Eigen::Matrix<double,1,-1> vec =
           Eigen::Matrix<double,1,-1>::Constant(N,
             std::numeric_limits<double>::quiet_NaN());
-        current_statement__ = 6;
+        current_statement__ = 7;
         {
           stan::math::profile<local_scalar_t__> profile__("test",
             const_cast<stan::math::profile_map&>(profiles__));
@@ -4279,23 +4285,28 @@ class copy_prop_profile_model final : public model_base_crtp<copy_prop_profile_m
               std::numeric_limits<double>::quiet_NaN());
           stan::model::assign(lcm_sym4__, stan::math::columns_dot_self(X),
             "assigning variable lcm_sym4__");
+          stan::model::assign(vec2, lcm_sym4__, "assigning variable vec2");
+          current_statement__ = 6;
+          stan::model::assign(vec, vec2, "assigning variable vec");
         }
-        lcm_sym5__ = stan::math::sum(lcm_sym4__);
-        lp_accum__.add(lcm_sym5__);
-        current_statement__ = 7;
+        current_statement__ = 8;
+        lp_accum__.add(stan::math::sum(vec));
+        current_statement__ = 9;
         stan::math::validate_non_negative_index("vec3", "N", N);
         Eigen::Matrix<double,1,-1> vec3 =
           Eigen::Matrix<double,1,-1>::Constant(N,
             std::numeric_limits<double>::quiet_NaN());
         {
-          current_statement__ = 9;
+          current_statement__ = 11;
           stan::math::validate_non_negative_index("vec4", "N", N);
-          Eigen::Matrix<double,1,-1> vec4 =
-            Eigen::Matrix<double,1,-1>::Constant(N,
-              std::numeric_limits<double>::quiet_NaN());
+          Eigen::Matrix<double,1,-1> vec4;
+          current_statement__ = 12;
+          stan::model::assign(vec4, lcm_sym4__, "assigning variable vec4");
+          current_statement__ = 13;
+          stan::model::assign(vec3, vec4, "assigning variable vec3");
         }
-        current_statement__ = 12;
-        lp_accum__.add(lcm_sym5__);
+        current_statement__ = 15;
+        lp_accum__.add(stan::math::sum(vec3));
       }
     } catch (const std::exception& e) {
       stan::lang::rethrow_located(e, locations_array__[current_statement__]);
@@ -4367,8 +4378,7 @@ class copy_prop_profile_model final : public model_base_crtp<copy_prop_profile_m
     (void) DUMMY_VAR__;
     try {
       int lcm_sym1__;
-      int pos__;
-      pos__ = 1;
+      int pos__ = std::numeric_limits<int>::min();
       Eigen::Matrix<local_scalar_t__,-1,-1> X =
         Eigen::Matrix<local_scalar_t__,-1,-1>::Constant(N, N, DUMMY_VAR__);
       lcm_sym1__ = stan::math::logical_gte(N, 1);
@@ -4413,10 +4423,10 @@ class copy_prop_profile_model final : public model_base_crtp<copy_prop_profile_m
   constrained_param_names(std::vector<std::string>& param_names__, bool
                           emit_transformed_parameters__ = true, bool
                           emit_generated_quantities__ = true) const final {
-    for (int sym6__ = 1; sym6__ <= N; ++sym6__) {
-      for (int sym7__ = 1; sym7__ <= N; ++sym7__) {
+    for (int sym7__ = 1; sym7__ <= N; ++sym7__) {
+      for (int sym8__ = 1; sym8__ <= N; ++sym8__) {
         param_names__.emplace_back(std::string() + "X" + '.' +
-          std::to_string(sym7__) + '.' + std::to_string(sym6__));
+          std::to_string(sym8__) + '.' + std::to_string(sym7__));
       }
     }
     if (emit_transformed_parameters__) {}
@@ -4426,10 +4436,10 @@ class copy_prop_profile_model final : public model_base_crtp<copy_prop_profile_m
   unconstrained_param_names(std::vector<std::string>& param_names__, bool
                             emit_transformed_parameters__ = true, bool
                             emit_generated_quantities__ = true) const final {
-    for (int sym6__ = 1; sym6__ <= N; ++sym6__) {
-      for (int sym7__ = 1; sym7__ <= N; ++sym7__) {
+    for (int sym7__ = 1; sym7__ <= N; ++sym7__) {
+      for (int sym8__ = 1; sym8__ <= N; ++sym8__) {
         param_names__.emplace_back(std::string() + "X" + '.' +
-          std::to_string(sym7__) + '.' + std::to_string(sym6__));
+          std::to_string(sym8__) + '.' + std::to_string(sym7__));
       }
     }
     if (emit_transformed_parameters__) {}
diff --git a/test/integration/good/compiler-optimizations/cppO1.expected b/test/integration/good/compiler-optimizations/cppO1.expected
index 167a95fdc0..a532e75cc3 100644
--- a/test/integration/good/compiler-optimizations/cppO1.expected
+++ b/test/integration/good/compiler-optimizations/cppO1.expected
@@ -1488,13 +1488,14 @@ namespace copy_prop_profile_model_namespace {
 using stan::model::model_base_crtp;
 using namespace stan::math;
 stan::math::profile_map profiles__;
-static constexpr std::array<const char*, 18> locations_array__ =
+static constexpr std::array<const char*, 19> locations_array__ =
   {" (found before start of program)",
   " (in 'copy-prop-profile.stan', line 5, column 2 to column 16)",
   " (in 'copy-prop-profile.stan', line 9, column 13 to column 14)",
   " (in 'copy-prop-profile.stan', line 9, column 2 to column 20)",
   " (in 'copy-prop-profile.stan', line 12, column 15 to column 16)",
   " (in 'copy-prop-profile.stan', line 12, column 4 to column 45)",
+  " (in 'copy-prop-profile.stan', line 13, column 4 to column 15)",
   " (in 'copy-prop-profile.stan', line 11, column 2 to line 14, column 3)",
   " (in 'copy-prop-profile.stan', line 16, column 2 to column 21)",
   " (in 'copy-prop-profile.stan', line 18, column 13 to column 14)",
@@ -1529,20 +1530,19 @@ class copy_prop_profile_model final : public model_base_crtp<copy_prop_profile_m
     // suppress unused var warning
     (void) DUMMY_VAR__;
     try {
-      int pos__;
-      pos__ = 1;
-      current_statement__ = 15;
+      int pos__ = std::numeric_limits<int>::min();
+      current_statement__ = 16;
       context__.validate_dims("data initialization", "N", "int",
         std::vector<size_t>{});
       N = std::numeric_limits<int>::min();
-      current_statement__ = 15;
+      current_statement__ = 16;
       N = context__.vals_i("N")[(1 - 1)];
-      current_statement__ = 15;
-      stan::math::check_greater_or_equal(function__, "N", N, 0);
       current_statement__ = 16;
-      stan::math::validate_non_negative_index("X", "N", N);
+      stan::math::check_greater_or_equal(function__, "N", N, 0);
       current_statement__ = 17;
       stan::math::validate_non_negative_index("X", "N", N);
+      current_statement__ = 18;
+      stan::math::validate_non_negative_index("X", "N", N);
     } catch (const std::exception& e) {
       stan::lang::rethrow_located(e, locations_array__[current_statement__]);
     }
@@ -1587,7 +1587,7 @@ class copy_prop_profile_model final : public model_base_crtp<copy_prop_profile_m
             Eigen::Matrix<local_scalar_t__,1,-1>>(Eigen::Matrix<double,1,-1>::Constant(N,
                                                     std::numeric_limits<double>::quiet_NaN(
                                                       )));
-        current_statement__ = 6;
+        current_statement__ = 7;
         {
           stan::math::profile<local_scalar_t__> profile__("test",
             const_cast<stan::math::profile_map&>(profiles__));
@@ -1597,24 +1597,30 @@ class copy_prop_profile_model final : public model_base_crtp<copy_prop_profile_m
           current_statement__ = 5;
           stan::model::assign(vec2, stan::math::columns_dot_self(X),
             "assigning variable vec2");
+          current_statement__ = 6;
+          stan::model::assign(vec, vec2, "assigning variable vec");
         }
-        current_statement__ = 7;
-        lp_accum__.add(stan::math::sum(vec2));
         current_statement__ = 8;
+        lp_accum__.add(stan::math::sum(vec));
+        current_statement__ = 9;
         stan::math::validate_non_negative_index("vec3", "N", N);
-        Eigen::Matrix<local_scalar_t__,1,-1> vec3 =
-          Eigen::Matrix<local_scalar_t__,1,-1>::Constant(N, DUMMY_VAR__);
+        stan::conditional_var_value_t<local_scalar_t__,
+          Eigen::Matrix<local_scalar_t__,1,-1>> vec3 =
+          stan::conditional_var_value_t<local_scalar_t__,
+            Eigen::Matrix<local_scalar_t__,1,-1>>(Eigen::Matrix<double,1,-1>::Constant(N,
+                                                    std::numeric_limits<double>::quiet_NaN(
+                                                      )));
         {
-          current_statement__ = 10;
+          current_statement__ = 11;
           stan::math::validate_non_negative_index("vec4", "N", N);
           Eigen::Matrix<local_scalar_t__,1,-1> vec4;
-          current_statement__ = 11;
+          current_statement__ = 12;
           stan::model::assign(vec4, stan::math::columns_dot_self(X),
             "assigning variable vec4");
-          current_statement__ = 12;
+          current_statement__ = 13;
           stan::model::assign(vec3, vec4, "assigning variable vec3");
         }
-        current_statement__ = 14;
+        current_statement__ = 15;
         lp_accum__.add(stan::math::sum(vec3));
       }
     } catch (const std::exception& e) {
@@ -1684,8 +1690,7 @@ class copy_prop_profile_model final : public model_base_crtp<copy_prop_profile_m
     // suppress unused var warning
     (void) DUMMY_VAR__;
     try {
-      int pos__;
-      pos__ = 1;
+      int pos__ = std::numeric_limits<int>::min();
       Eigen::Matrix<local_scalar_t__,-1,-1> X =
         Eigen::Matrix<local_scalar_t__,-1,-1>::Constant(N, N, DUMMY_VAR__);
       for (int sym1__ = 1; sym1__ <= N; ++sym1__) {