diff --git a/lib/ModelingToolkitTearing/src/ModelingToolkitTearing.jl b/lib/ModelingToolkitTearing/src/ModelingToolkitTearing.jl
index 23046ae..d2d8b73 100644
--- a/lib/ModelingToolkitTearing/src/ModelingToolkitTearing.jl
+++ b/lib/ModelingToolkitTearing/src/ModelingToolkitTearing.jl
@@ -107,7 +107,7 @@ function MTKBase.unhack_system(sys::System)
     resize!(obs_mask, length(obseqs))
     fill!(obs_mask, true)
     additional_eqs = Equation[]
-    additional_vars = SymbolicT[]
+    additional_vars = Set{SymbolicT}()
     additional_subs = Dict{SymbolicT, SymbolicT}()
 
     # Also need to update schedule
@@ -142,21 +142,15 @@ function MTKBase.unhack_system(sys::System)
 
         resid = A * x - b
         for res in resid
+            SU._iszero(res) && continue
+            # If a linear SCC contains both `D(w)` and `w_t`, it'll contain the equation `D(w) ~ w_t`.
+            # When unhacking it, `D(w)` will be totermed into `w_t`. Avoid adding the `0 ~ 0` equations.
+            # The duplicate variables are automatically removed by the `Set`.
+            # See https://github.com/SciML/ModelingToolkit.jl/issues/4196 for further details.
             push!(additional_eqs, Symbolics.COMMON_ZERO ~ res)
         end
     end
     @assert length(additional_eqs) == length(additional_vars)
-    # If a linear SCC contains both `D(w)` and `w_t`, it'll contain the equation `D(w) ~ w_t`.
-    # When unhacking it, `D(w)` will be totermed into `w_t`. This, `additional_vars` contains
-    # two `w_t` and an equation that is `0 ~ 0`. Find the `0 ~ 0` equations, and remove them
-    # along with the duplicate variables.
-    # See https://github.com/SciML/ModelingToolkit.jl/issues/4196 for further details.
-    additional_eqs_mask = trues(length(additional_eqs))
-    for (i, eq) in enumerate(additional_eqs)
-        additional_eqs_mask[i] = !SU._iszero(eq.rhs)
-    end
-    additional_eqs = additional_eqs[additional_eqs_mask]
-    additional_vars = additional_vars[additional_eqs_mask]
     subst = SU.Substituter{false}(additional_subs, SU.default_substitute_filter)
     obseqs = obseqs[obs_mask]
     map!(subst, obseqs, obseqs)
@@ -167,7 +161,7 @@ function MTKBase.unhack_system(sys::System)
         map!(subst, values(sched.dummy_sub))
     end
 
-    dvs = [unknowns(sys); additional_vars]
+    dvs = [unknowns(sys); collect(additional_vars)]
 
     newsys = @set sys.observed = obseqs
     @set! newsys.eqs = eqs