diff --git a/src/StructuralIdentifiability.jl b/src/StructuralIdentifiability.jl
index 4536f845b..636a39ef8 100644
--- a/src/StructuralIdentifiability.jl
+++ b/src/StructuralIdentifiability.jl
@@ -131,6 +131,7 @@ include("global_identifiability.jl")
 include("identifiable_functions.jl")
 include("observation_field.jl")
 include("parametrizations.jl")
+include("weights.jl")
 include("lincomp.jl")
 include("pb_representation.jl")
 include("submodels.jl")
diff --git a/src/weights.jl b/src/weights.jl
new file mode 100644
index 000000000..146499a3e
--- /dev/null
+++ b/src/weights.jl
@@ -0,0 +1,62 @@
+"""
+    cmp_weighted(ode, W)
+
+Comparator with arbitrary weights.
+"""
+function cmp_weighted(ode, W::Matrix{Int})
+    @assert all(>=(0), W) "Weights must be non-negative."
+    states, params = ode.x_vars, ode.parameters
+    df(f) = lie_derivative(f, ode)
+    features(f) = [
+        !iszero(f),
+        total_degree(denominator(f)),
+        total_degree(numerator(f)),
+        length(numerator(f)) + length(denominator(f)),
+        !issubset(vars(f), params),
+        total_degree_wrt(numerator(f), states),
+        total_degree_wrt(denominator(f), states),
+        number_of_terms(f, states),
+
+        # Lie derivative
+        !iszero(df(f)),
+        total_degree(numerator(df(f))),
+        total_degree(denominator(df(f))),
+        length(numerator(df(f))) + length(denominator(df(f))),
+        total_degree_wrt(df(f), states),
+        total_degree_wrt(denominator(df(f)), states),
+        number_of_terms(df(f), states),
+    ]
+
+    fallback = rational_function_cmp
+    cmp = function (f, g)
+        f = parent_ring_change(f, parent(ode))
+        g = parent_ring_change(g, parent(ode))
+        v_f = features(f)
+        v_g = features(g)
+        score_f = W * v_f
+        score_g = W * v_g
+        score_f != score_g && return score_f < score_g
+        return fallback(f, g)
+    end
+    return cmp
+end
+
+# Matrices of weights for existing named comparators.
+const matrix_comparators = let
+    row(indices...) = [Int(j in indices) for _ in 1:1, j in 1:15]
+    ordinary = vcat(row(1), row(2, 3), row(4), row(2))
+    state = vcat(row(6, 7), row(7), row(8))
+    lie = vcat(row(9), row(10, 11), row(12), row(11))
+    lie_state = vcat(row(13), row(14), row(15))
+    parameter_first = vcat(row(5), ordinary)
+
+    matrices = Dict(
+        cmp_default => parameter_first,
+        cmp_lie => lie,
+        cmp_states => vcat(state, ordinary),
+        cmp_lie_states => vcat(lie_state, lie),
+        cmp_pushka => vcat(state, lie_state, lie),
+    )
+    nrows = maximum(size(W, 1) for W in values(matrices))
+    Dict(cmp => vcat(W, zeros(Int, nrows - size(W, 1), 15)) for (cmp, W) in matrices)
+end