diff --git a/src/constraint_tree.jl b/src/constraint_tree.jl
index 2fb4a03..d9061f2 100644
--- a/src/constraint_tree.jl
+++ b/src/constraint_tree.jl
@@ -14,7 +14,7 @@
 # See the License for the specific language governing permissions and
 # limitations under the License.
 
-import DataStructures: SortedDict
+import DataStructures: SortedDict, SortedSet
 
 """
 $(TYPEDEF)
@@ -98,7 +98,7 @@ $(TYPEDSIGNATURES)
 
 Find the expected count of variables in a [`ConstraintTree`](@ref).
 """
-var_count(x::ConstraintTree) = isempty(elems(x)) ? 0 : maximum(var_count.(values(elems(x))))
+var_count(x::ConstraintTree) = isempty(elems(x)) ? 0 : maximum(var_count.(values(x)))
 
 """
 $(TYPEDSIGNATURES)
@@ -159,6 +159,65 @@ incr_var_idxs(x::QuadraticValue, incr::Int) = QuadraticValue(
     weights = x.weights,
 )
 
+"""
+$(TYPEDSIGNATURES)
+
+Push all variable indexes found in `x` to the `out` container.
+
+(The container needs to support the standard `push!`.)
+"""
+collect_variables!(x::Constraint, out) = collect_variables!(x.value)
+collect_variables!(x::LinearValue, out) =
+    for idx in x.idxs
+        push!(out, idx)
+    end
+collect_variables!(x::QuadraticValue, out) =
+    for (idx, idy) in x.idxs
+        push!(out, idx, idy)
+    end
+collect_variables!(x::ConstraintTree, out) = collect_variables!.(values(x), Ref(out))
+
+"""
+$(TYPEDSIGNATURES)
+
+Prune the unused variable indexes from an object `x` (such as a
+[`ConstraintTree`](@ref)).
+
+This first runs [`collect_variables!`](@ref) to determine the actual used
+variables, then calls [`renumber_variables`](@ref) to create a renumbered
+object.
+"""
+function prune_variables(x)
+    vars = SortedSet{Int}()
+    collect_variables!(x, vars)
+    push!(vars, 0)
+    vv = collect(vars)
+    @assert vv[1] == 0 "variable indexes are broken"
+    return renumber_variables(x, SortedDict(vv .=> 0:length(vv)))
+end
+
+"""
+$(TYPEDSIGNATURES)
+
+Renumber all variables in an object (such as [`ConstraintTree`](@ref)). The new
+variable indexes are taken from the `mapping` parameter at the index of the old
+variable's index.
+
+This does not run any consistency checks on the result; the `mapping` must
+therefore be monotonically increasing, and the zero index must map to itself,
+otherwise invalid [`Value`](@ref)s will be produced.
+"""
+renumber_variables(x::ConstraintTree, mapping) =
+    ConstraintTree(k => renumber_Variables(v, mapping) for (k, v) in x)
+renumber_variables(x::Constraint, mapping) =
+    Constraint(renumber_variables(x.value, mapping), x.bound)
+renumber_variables(x::LinearValue, mapping) =
+    LinearValue(idxs = [mapping[idx] for idx in x.idxs], weights = x.weights)
+renumber_variables(x::QuadraticValue, mapping) = QuadraticValue(
+    idxs = [(mapping[idx], mapping[idy]) for (idx, idy) in x.idxs],
+    weights = x.weights,
+)
+
 #
 # Algebraic construction
 #