diff --git a/src/structural_transformation/utils.jl b/src/structural_transformation/utils.jl
index 405a3ebed3..bd24a1d017 100644
--- a/src/structural_transformation/utils.jl
+++ b/src/structural_transformation/utils.jl
@@ -123,16 +123,15 @@ function check_consistency(state::TransformationState, orig_inputs; nothrow = fa
     unassigned_var = singular_check(state)
 
     if !isempty(unassigned_var) || !is_balanced
+        if nothrow
+            return false
+        end
         io = IOBuffer()
         Base.print_array(io, unassigned_var)
         unassigned_var_str = String(take!(io))
         errmsg = "The system is structurally singular! " *
                  "Here are the problematic variables: \n" *
                  unassigned_var_str
-        if nothrow
-            @warn errmsg
-            return false
-        end
         throw(InvalidSystemException(errmsg))
     end
 
diff --git a/src/systems/diffeqs/abstractodesystem.jl b/src/systems/diffeqs/abstractodesystem.jl
index 4019a868d8..8f70f6710d 100644
--- a/src/systems/diffeqs/abstractodesystem.jl
+++ b/src/systems/diffeqs/abstractodesystem.jl
@@ -1313,8 +1313,15 @@ function InitializationProblem{iip, specialize}(sys::AbstractODESystem,
                 sys; u0map, initialization_eqs, check_units, pmap = parammap); fully_determined)
     end
 
-    if !isempty(StructuralTransformations.singular_check(get_tearing_state(isys)))
-        @warn "Since the initialization system is singular, the guess values may significantly affect the initial values of the ODE"
+    ts = get_tearing_state(isys)
+    if warn_initialize_determined && (unassigned_vars = StructuralTransformations.singular_check(ts); !isempty(unassigned_vars))
+        errmsg = """
+        The initialization system is singular. Guess values may significantly affect \
+        the initial values of the ODE. The problematic variables are $unassigned_vars.
+
+        Note that the identification of problematic variables is a best-effort heuristic.
+        """
+        @warn errmsg
     end
 
     uninit = setdiff(unknowns(sys), [unknowns(isys); getfield.(observed(isys), :lhs)])