diff --git a/gpkit/constraints/costed.py b/gpkit/constraints/costed.py
index 09f93a3e9..70901a97f 100644
--- a/gpkit/constraints/costed.py
+++ b/gpkit/constraints/costed.py
@@ -24,10 +24,11 @@ def subinplace(self, subs):
         self.cost = self.cost.sub(subs)
         ConstraintSet.subinplace(self, subs)
 
-    @property
-    def varkeys(self):
-        "return all Varkeys present in this ConstraintSet"
-        return ConstraintSet._varkeys(self, self.cost.varlocs)
+    def reset_varkeys(self, init_dict=None):
+        "Resets varkeys to what is in the cost and constraints"
+        ConstraintSet.reset_varkeys(self, self.cost.varlocs)
+        if init_dict is not None:
+            self.varkeys.update(init_dict)
 
     def rootconstr_str(self, excluded=None):
         "The appearance of a ConstraintSet in addition to its contents"
diff --git a/gpkit/constraints/linked.py b/gpkit/constraints/linked.py
index 340bc461e..d9b1d9c29 100644
--- a/gpkit/constraints/linked.py
+++ b/gpkit/constraints/linked.py
@@ -27,11 +27,10 @@ class LinkedConstraintSet(ConstraintSet):
     """
     def __init__(self, constraints, include_only=None, exclude=None):
         ConstraintSet.__init__(self, constraints)
-        varkeys = self.varkeys
         linkable = set()
-        for varkey in varkeys:
+        for varkey in self.varkeys:
             name_without_model = varkey.str_without(["models"])
-            if len(varkeys[name_without_model]) > 1:
+            if len(self.varkeys[name_without_model]) > 1:
                 linkable.add(name_without_model)
         if include_only:
             linkable &= set(include_only)
@@ -39,7 +38,7 @@ def __init__(self, constraints, include_only=None, exclude=None):
             linkable -= set(exclude)
         self.linked, self.reverselinks = {}, {}
         for name in linkable:
-            vks = varkeys[name]
+            vks = self.varkeys[name]
             sub, subbed_vk = None, None
             for vk in vks:
                 if vk in self.substitutions:
@@ -66,6 +65,10 @@ def __init__(self, constraints, include_only=None, exclude=None):
             self.reverselinks[newvk] = vks
         with SignomialsEnabled():  # since we're just substituting varkeys.
             self.subinplace(self.linked)
+        for constraint in self:
+            if hasattr(constraint, "reset_varkeys"):
+                constraint.reset_varkeys()
+        self.reset_varkeys()
 
     def process_result(self, result):
         super(LinkedConstraintSet, self).process_result(result)
diff --git a/gpkit/constraints/prog_factories.py b/gpkit/constraints/prog_factories.py
index 01e89fc1c..2cc599af7 100644
--- a/gpkit/constraints/prog_factories.py
+++ b/gpkit/constraints/prog_factories.py
@@ -1,10 +1,6 @@
 "Scripts for generating, solving and sweeping programs"
 from time import time
 import numpy as np
-from ..nomials.substitution import parse_subs
-from ..solution_array import SolutionArray
-from ..keydict import KeyDict
-from ..varkey import VarKey
 
 try:
     from ipyparallel import Client
@@ -16,6 +12,11 @@
 except (ImportError, IOError, AssertionError):
     POOL = None
 
+from ..nomials.substitution import parse_subs
+from ..solution_array import SolutionArray
+from ..keydict import KeyDict
+from ..varkey import VarKey
+
 
 def _progify_fctry(program, return_attr=None):
     "Generates function that returns a program() and optionally an attribute."
diff --git a/gpkit/constraints/set.py b/gpkit/constraints/set.py
index 83d72cc88..33de27811 100644
--- a/gpkit/constraints/set.py
+++ b/gpkit/constraints/set.py
@@ -18,6 +18,7 @@ def __init__(self, constraints, substitutions=None, recursesubs=True):
             constraints = [constraints]
         list.__init__(self, constraints)
         subs = substitutions if substitutions else {}
+        self.unused_variables = None
         if not isinstance(constraints, ConstraintSet):
             # constraintsetify everything
             for i, constraint in enumerate(self):
@@ -28,6 +29,7 @@ def __init__(self, constraints, substitutions=None, recursesubs=True):
             # grab the substitutions dict from the top constraintset
             subs.update(constraints.substitutions)  # pylint: disable=no-member
         if recursesubs:
+            self.reset_varkeys()
             self.substitutions = KeyDict.with_keys(self.varkeys,
                                                    self._iter_subs(subs))
         else:
@@ -47,6 +49,10 @@ def __getitem__(self, key):
                 variables.sort(key=_var_sort_key)
                 return variables
 
+    def __setitem__(self, key, value):
+        list.__setitem__(self, key, value)
+        self.reset_varkeys()
+
     __str__ = _str
     __repr__ = _repr
     _repr_latex_ = _repr_latex_
@@ -126,20 +132,27 @@ def subinplace(self, subs):
         "Substitutes in place."
         for constraint in self:
             constraint.subinplace(subs)
-
-    @property
-    def varkeys(self):
-        "return all Varkeys present in this ConstraintSet"
-        return self._varkeys()
-
-    def _varkeys(self, init_dict=None):
-        "return all Varkeys present in this ConstraintSet"
-        init_dict = {} if init_dict is None else init_dict
-        out = KeySet(init_dict)
+        if self.unused_variables is not None:
+            unused_vars = []
+            for var in self.unused_variables:
+                if var.key in subs:
+                    unused_vars.append(subs[var.key])
+                else:
+                    unused_vars.append(var.key)
+            self.unused_variables = unused_vars
+        self.reset_varkeys()
+
+    def reset_varkeys(self, init_dict=None):
+        "Goes through constraints and collects their varkeys."
+        varkeys = KeySet()
+        if init_dict is not None:
+            varkeys.update(init_dict)
         for constraint in self:
             if hasattr(constraint, "varkeys"):
-                out.update(constraint.varkeys)
-        return out
+                varkeys.update(constraint.varkeys)
+        if self.unused_variables is not None:
+            varkeys.update(self.unused_variables)
+        self.varkeys = varkeys
 
     def as_posyslt1(self):
         "Returns list of posynomials which must be kept <= 1"
diff --git a/gpkit/keydict.py b/gpkit/keydict.py
index aba2fe594..d39af3c1c 100644
--- a/gpkit/keydict.py
+++ b/gpkit/keydict.py
@@ -149,6 +149,19 @@ class KeySet(KeyDict):
     "KeySets are KeyDicts without values, serving only to filter and map keys"
     collapse_arrays = False
 
+    def add(self, item):
+        "Adds an item to the keyset"
+        self[item] = None
+
+    def update(self, *args, **kwargs):
+        "Iterates through the dictionary created by args and kwargs"
+        if len(args) == 1:
+            for item in args[0]:
+                self.add(item)
+        else:
+            for k, v in dict(*args, **kwargs).items():
+                self[k] = v
+
     def __getitem__(self, key):
         "Gets the keys corresponding to a particular key."
         key, _ = self.parse_and_index(key)
diff --git a/gpkit/tests/t_model.py b/gpkit/tests/t_model.py
index d44161c97..3c5b51fa3 100644
--- a/gpkit/tests/t_model.py
+++ b/gpkit/tests/t_model.py
@@ -418,7 +418,24 @@ def test_cvxopt_kwargs(self):
         self.assertAlmostEqual(sol["cost"], 12., NDIGS["cvxopt"])
 
 
-TESTS = [TestModelSolverSpecific]
+class Thing(Model):
+    "a thing, for model testing"
+    def __init__(self, n, **kwargs):
+        a = VectorVariable(n, "a", "g/m")
+        b = VectorVariable(n, "b", "m")
+        c = Variable("c", 17/4., "g")
+        Model.__init__(self, None, [a >= c/b], **kwargs)
+
+
+class TestModelNoSolve(unittest.TestCase):
+    """model tests that don't require a solver"""
+    def test_modelname_added(self):
+        t = Thing(2)
+        for vk in t.varkeys:
+            self.assertEqual(vk.models, ["Thing"])
+
+
+TESTS = [TestModelSolverSpecific, TestModelNoSolve]
 MULTI_SOLVER_TESTS = [TestGP, TestSP]
 
 for testcase in MULTI_SOLVER_TESTS: