diff --git a/src/structural_transformation/bipartite_tearing/modia_tearing.jl b/src/structural_transformation/bipartite_tearing/modia_tearing.jl
index e8304752e8..90c1d1f367 100644
--- a/src/structural_transformation/bipartite_tearing/modia_tearing.jl
+++ b/src/structural_transformation/bipartite_tearing/modia_tearing.jl
@@ -1,6 +1,31 @@
 # This code is derived from the Modia project and is licensed as follows:
 # https://github.com/ModiaSim/Modia.jl/blob/b61daad643ef7edd0c1ccce6bf462c6acfb4ad1a/LICENSE
 
+struct OrderedBitSet <: AbstractSet{Int}
+    bitset::BitSet
+    order::Vector{Int}
+end
+OrderedBitSet() = OrderedBitSet(BitSet(), Int[])
+Base.iterate(o::OrderedBitSet) = Base.iterate(o.order)
+Base.iterate(o::OrderedBitSet, state) = Base.iterate(o.order, state)
+Base.in(a::Int, o::OrderedBitSet) = a in o.bitset
+function Base.push!(o::OrderedBitSet, a::Int)
+    if !(a in o.bitset)
+        push!(o.bitset, a)
+        push!(o.order, a)
+    end
+    o
+end
+function Base.empty!(o::OrderedBitSet)
+    empty!(o.bitset)
+    empty!(o.order)
+    o
+end
+function Base.sort!(o::OrderedBitSet; kw...)
+    sort!(o.order; kw...)
+    o
+end
+
 function try_assign_eq!(ict::IncrementalCycleTracker, vj::Integer, eq::Integer)
     G = ict.graph
     add_edge_checked!(ict, Iterators.filter(!=(vj), 𝑠neighbors(G.graph, eq)), vj) do G
@@ -20,7 +45,7 @@ function try_assign_eq!(ict::IncrementalCycleTracker, vars, v_active, eq::Intege
 end
 
 function tearEquations!(ict::IncrementalCycleTracker, Gsolvable, es::Vector{Int},
-    v_active::BitSet, isder′::F) where {F}
+    v_active::OrderedBitSet, isder′::F) where {F}
     check_der = isder′ !== nothing
     if check_der
         has_der = Ref(false)
@@ -54,10 +79,13 @@ function tearEquations!(ict::IncrementalCycleTracker, Gsolvable, es::Vector{Int}
 end
 
 function tear_graph_block_modia!(var_eq_matching, ict, solvable_graph, eqs, vars,
-    isder::F) where {F}
+    isder::F, solved_eq) where {F}
     tearEquations!(ict, solvable_graph.fadjlist, eqs, vars, isder)
     for var in vars
-        var_eq_matching[var] = ict.graph.matching[var]
+        eq = var_eq_matching[var] = ict.graph.matching[var]
+        if eq isa Int
+            push!(solved_eq, eq)
+        end
     end
     return nothing
 end
@@ -65,7 +93,8 @@ end
 function tear_graph_modia(structure::SystemStructure, isder::F = nothing,
     ::Type{U} = Unassigned;
     varfilter::F2 = v -> true,
-    eqfilter::F3 = eq -> true) where {F, U, F2, F3}
+    eqfilter::F3 = eq -> true,
+    state_priority::F4 = nothing) where {F, U, F2, F3, F4}
     # It would be possible here to simply iterate over all variables and attempt to
     # use tearEquations! to produce a matching that greedily selects the minimal
     # number of torn variables. However, we can do this process faster if we first
@@ -88,20 +117,29 @@ function tear_graph_modia(structure::SystemStructure, isder::F = nothing,
     ict = IncrementalCycleTracker(vargraph; dir = :in)
 
     ieqs = Int[]
-    filtered_vars = BitSet()
+    filtered_vars = OrderedBitSet()
+    solved_eq = BitSet()
+    if state_priority !== nothing
+        sort!(var_sccs, by = Base.Fix1(sum, state_priority))
+    end
     for vars in var_sccs
         for var in vars
             if varfilter(var)
                 push!(filtered_vars, var)
-                if var_eq_matching[var] !== unassigned
-                    push!(ieqs, var_eq_matching[var])
+                for eq in 𝑑neighbors(graph, var)
+                    if !(eq in solved_eq)
+                        push!(ieqs, eq)
+                    end
                 end
             end
             var_eq_matching[var] = unassigned
         end
+        if state_priority !== nothing
+            sort!(filtered_vars, by = state_priority)
+        end
         tear_graph_block_modia!(var_eq_matching, ict, solvable_graph, ieqs,
             filtered_vars,
-            isder)
+            isder, solved_eq)
 
         # clear cache
         vargraph.ne = 0
diff --git a/src/structural_transformation/partial_state_selection.jl b/src/structural_transformation/partial_state_selection.jl
index f2fec0269f..6b2ed3ac71 100644
--- a/src/structural_transformation/partial_state_selection.jl
+++ b/src/structural_transformation/partial_state_selection.jl
@@ -340,7 +340,7 @@ function dummy_derivative_graph!(structure::SystemStructure, var_eq_matching, ja
 
     var_eq_matching, full_var_eq_matching = tear_graph_modia(structure, isdiffed,
         Union{Unassigned, SelectedState};
-        varfilter = can_eliminate)
+        varfilter = can_eliminate, state_priority)
     for v in eachindex(var_eq_matching)
         is_not_present(v) && continue
         dv = var_to_diff[v]
diff --git a/src/systems/abstractsystem.jl b/src/systems/abstractsystem.jl
index 83a28a259c..533d93e400 100644
--- a/src/systems/abstractsystem.jl
+++ b/src/systems/abstractsystem.jl
@@ -1452,6 +1452,17 @@ function markio!(state, orig_inputs, inputs, outputs; check = true)
     state, orig_inputs
 end
 
+function set_priorities!(state, priorities)
+    fullvars = state.fullvars
+    prio_dict = Dict(priorities)
+    for (i, v) in enumerate(fullvars)
+        p = get(prio_dict, v, nothing)
+        p === nothing && continue
+        v = setmetadata(v, VariableStatePriority, p)
+        fullvars[i] = v
+    end
+end
+
 """
     (; A, B, C, D), simplified_sys = linearize(sys, inputs, outputs;    t=0.0, op = Dict(), allow_input_derivatives = false, zero_dummy_der=false, kwargs...)
     (; A, B, C, D)                 = linearize(simplified_sys, lin_fun; t=0.0, op = Dict(), allow_input_derivatives = false, zero_dummy_der=false)
diff --git a/src/systems/systemstructure.jl b/src/systems/systemstructure.jl
index 4e330619d5..3e1467eb6b 100644
--- a/src/systems/systemstructure.jl
+++ b/src/systems/systemstructure.jl
@@ -599,13 +599,14 @@ end
 
 function _structural_simplify!(state::TearingState, io; simplify = false,
     check_consistency = true, fully_determined = true,
-    kwargs...)
+    priorities = Dict(), kwargs...)
     check_consistency &= fully_determined
     has_io = io !== nothing
     orig_inputs = Set()
     if has_io
         ModelingToolkit.markio!(state, orig_inputs, io...)
     end
+    isempty(priorities) || ModelingToolkit.set_priorities!(state, priorities)
     state, input_idxs = ModelingToolkit.inputs_to_parameters!(state, io)
     sys, mm = ModelingToolkit.alias_elimination!(state; kwargs...)
     if check_consistency
diff --git a/test/structural_transformation/tearing.jl b/test/structural_transformation/tearing.jl
index a30238a645..eed5f91aec 100644
--- a/test/structural_transformation/tearing.jl
+++ b/test/structural_transformation/tearing.jl
@@ -219,3 +219,52 @@ sys = structural_simplify(ms_model)
 prob_complex = ODAEProblem(sys, u0, (0, 1.0))
 sol = solve(prob_complex, Tsit5())
 @test all(sol[mass.v] .== 1)
+
+## Test priorities
+@parameters t
+D = Differential(t)
+
+function Cart(; init_pos, init_vel, mass, name = :cart)
+    @variables pos(t)=init_pos vel(t)=init_vel
+    @variables f(t)
+    @parameters mass = mass
+
+    eqs = [D(pos) ~ vel
+        D(vel) ~ f / mass]
+
+    return ODESystem(eqs; name)
+end
+
+function PDController(; kp = 0, kd = 0, name = :controller)
+    @variables x(t) v(t) f(t)
+    @parameters kp=kp kd=kd
+
+    eqs = [
+        f ~ -kp * x - kd * v,
+    ]
+
+    return ODESystem(eqs; name)
+end
+
+function ControlledCart(; cart, cont, name = :sys)
+    eqs = [cart.pos ~ cont.x
+        cart.vel ~ cont.v
+        cart.f ~ cont.f]
+    return ODESystem(eqs; name, systems = [cart, cont])
+end
+
+cart = Cart(init_pos = 0.0, init_vel = 1.0, mass = 0.5)
+cont = PDController(kp = 1.0, kd = 0.5)
+controlled_cart = ControlledCart(; cart, cont)
+@variables z(t) k(t)
+eqs = [z ~ k;
+    sqrt(z) ~ abs(cont.x)]
+@named alge = ODESystem(eqs, t);
+controlled_cart = extend(controlled_cart, alge)
+# Test that our state priorities are respected
+s1 = states(structural_simplify(controlled_cart,
+    priorities = [k => 2]))
+s2 = states(structural_simplify(controlled_cart,
+    priorities = [z => 2]))
+@test Set(s1) == Set([cart.pos, cart.vel, k])
+@test Set(s2) == Set([cart.pos, cart.vel, z])