diff --git a/src/systems/alias_elimination.jl b/src/systems/alias_elimination.jl
index fb4fedc920..e0bfde2268 100644
--- a/src/systems/alias_elimination.jl
+++ b/src/systems/alias_elimination.jl
@@ -8,7 +8,7 @@ function alias_eliminate_graph!(state::TransformationState; kwargs...)
     end
 
     @unpack graph, var_to_diff, solvable_graph = state.structure
-    mm = alias_eliminate_graph!(state, mm)
+    mm = alias_eliminate_graph!(state, mm; kwargs...)
     s = state.structure
     for g in (s.graph, s.solvable_graph)
         g === nothing && continue
@@ -347,7 +347,7 @@ function do_bareiss!(M, Mold, is_linear_variables, is_highest_diff)
     (rank1, rank2, rank3, pivots)
 end
 
-function alias_eliminate_graph!(state::TransformationState, ils::SparseMatrixCLIL)
+function alias_eliminate_graph!(state::TransformationState, ils::SparseMatrixCLIL; fully_determined = true, kwargs...)
     @unpack structure = state
     @unpack graph, solvable_graph, var_to_diff, eq_to_diff = state.structure
     # Step 1: Perform Bareiss factorization on the adjacency matrix of the linear
@@ -355,19 +355,21 @@ function alias_eliminate_graph!(state::TransformationState, ils::SparseMatrixCLI
     #
     ils, solvable_variables, (rank1, rank2, rank3, pivots) = aag_bareiss!(structure, ils)
 
-    ## Step 2: Simplify the system using the Bareiss factorization
-    rk1vars = BitSet(@view pivots[1:rank1])
-    for v in solvable_variables
-        v in rk1vars && continue
-        @set! ils.nparentrows += 1
-        push!(ils.nzrows, ils.nparentrows)
-        push!(ils.row_cols, [v])
-        push!(ils.row_vals, [convert(eltype(ils), 1)])
-        add_vertex!(graph, SRC)
-        add_vertex!(solvable_graph, SRC)
-        add_edge!(graph, ils.nparentrows, v)
-        add_edge!(solvable_graph, ils.nparentrows, v)
-        add_vertex!(eq_to_diff)
+    if fully_determined == true
+        ## Step 2: Simplify the system using the Bareiss factorization
+        rk1vars = BitSet(@view pivots[1:rank1])
+        for v in solvable_variables
+            v in rk1vars && continue
+            @set! ils.nparentrows += 1
+            push!(ils.nzrows, ils.nparentrows)
+            push!(ils.row_cols, [v])
+            push!(ils.row_vals, [convert(eltype(ils), 1)])
+            add_vertex!(graph, SRC)
+            add_vertex!(solvable_graph, SRC)
+            add_edge!(graph, ils.nparentrows, v)
+            add_edge!(solvable_graph, ils.nparentrows, v)
+            add_vertex!(eq_to_diff)
+        end
     end
 
     return ils
diff --git a/src/systems/systemstructure.jl b/src/systems/systemstructure.jl
index e368641350..71f996f251 100644
--- a/src/systems/systemstructure.jl
+++ b/src/systems/systemstructure.jl
@@ -753,7 +753,7 @@ function _mtkcompile!(state::TearingState; simplify = false,
         ModelingToolkit.markio!(state, orig_inputs, inputs, outputs, disturbance_inputs)
         state = ModelingToolkit.inputs_to_parameters!(state, [inputs; disturbance_inputs])
     end
-    sys, mm = ModelingToolkit.alias_elimination!(state; kwargs...)
+    sys, mm = ModelingToolkit.alias_elimination!(state; fully_determined, kwargs...)
     if check_consistency
         fully_determined = ModelingToolkit.check_consistency(
             state, orig_inputs; nothrow = fully_determined === nothing)
@@ -765,7 +765,7 @@ function _mtkcompile!(state::TearingState; simplify = false,
         var_eq_matching = pantelides!(state; finalize = false, kwargs...)
         sys = pantelides_reassemble(state, var_eq_matching)
         state = TearingState(sys)
-        sys, mm = ModelingToolkit.alias_elimination!(state; kwargs...)
+        sys, mm = ModelingToolkit.alias_elimination!(state; fully_determined, kwargs...)
         sys = ModelingToolkit.dummy_derivative(
             sys, state; simplify, mm, check_consistency, fully_determined, kwargs...)
     else
diff --git a/test/initializationsystem.jl b/test/initializationsystem.jl
index 06d0752076..e34641bbb2 100644
--- a/test/initializationsystem.jl
+++ b/test/initializationsystem.jl
@@ -455,14 +455,13 @@ sol = solve(prob, Tsit5())
 # Initialize with an observed variable
 prob = ODEProblem(simpsys, [z => 0.0], tspan, guesses = [x => 2.0, y => 4.0])
 sol = solve(prob, Tsit5())
-@test sol.u[1] == [0.0, 0.0]
+@test sol[z, 1] == 0.0
 
 prob = ODEProblem(simpsys, [z => 1.0, y => 1.0], tspan, guesses = [x => 2.0])
 sol = solve(prob, Tsit5())
 @test sol[[x, y], 1] == [0.0, 1.0]
 
-# This should warn, but logging tests can't be marked as broken
-@test_logs prob = ODEProblem(simpsys, [], tspan, guesses = [x => 2.0])
+@test_warn "underdetermined" prob = ODEProblem(simpsys, [], tspan, guesses = [x => 2.0, y => 1.0])
 
 # Late Binding initialization_eqs
 # https://github.com/SciML/ModelingToolkit.jl/issues/2787
diff --git a/test/symbolic_events.jl b/test/symbolic_events.jl
index d82bf8a5c1..e48f793a70 100644
--- a/test/symbolic_events.jl
+++ b/test/symbolic_events.jl
@@ -1368,7 +1368,7 @@ end
         D(x) ~ p2,
         x2 ~ p_1(x)
     ]
-    @mtkcompile sys = ODESystem(eq, t, [x, x2], [p_1, p2], discrete_events = [event])
+    @mtkcompile sys = System(eq, t, [x, x2], [p_1, p2], discrete_events = [event])
 
     prob = ODEProblem(sys, [], (0.0, 1.0))
     sol = solve(prob)