diff --git a/packages/swingset-liveslots/src/collectionManager.js b/packages/swingset-liveslots/src/collectionManager.js
index fb63f280ff4..4bbc74b21f0 100644
--- a/packages/swingset-liveslots/src/collectionManager.js
+++ b/packages/swingset-liveslots/src/collectionManager.js
@@ -685,7 +685,11 @@ export function makeCollectionManager(
     const collectionID = `${subid}`;
     const collection = summonCollectionInternal(false, collectionID, kindName);
 
-    const doMoreGC = collection.clearInternal(true);
+    let doMoreGC = collection.clearInternal(true);
+    const { schemataCapData } = schemaCache.get(collectionID);
+    doMoreGC =
+      schemataCapData.slots.map(vrm.removeReachableVref).some(b => b) ||
+      doMoreGC;
     for (const dbKey of enumerateKeysWithPrefix(
       syscall,
       prefixc(collectionID, '|'),
@@ -728,6 +732,15 @@ export function makeCollectionManager(
       schemata.valueShape = valueShape;
     }
     const schemataCapData = serialize(harden(schemata));
+    if (isDurable) {
+      schemataCapData.slots.forEach((vref, slotIndex) => {
+        if (!vrm.isDurable(vref)) {
+          throwNotDurable(vref, slotIndex, schemataCapData);
+        }
+      });
+    }
+    schemataCapData.slots.forEach(vrm.addReachableVref);
+
     schemaCache.set(
       collectionID,
       harden({ keyShape, valueShape, label, schemataCapData }),
diff --git a/packages/swingset-liveslots/test/test-collection-schema-refcount.js b/packages/swingset-liveslots/test/test-collection-schema-refcount.js
new file mode 100644
index 00000000000..03db7d350a4
--- /dev/null
+++ b/packages/swingset-liveslots/test/test-collection-schema-refcount.js
@@ -0,0 +1,106 @@
+import test from 'ava';
+import '@endo/init/debug.js';
+
+import { Far } from '@endo/marshal';
+import { makeLiveSlots } from '../src/liveslots.js';
+import { parseVatSlot } from '../src/parseVatSlots.js';
+import { kser } from './kmarshal.js';
+import { buildSyscall } from './liveslots-helpers.js';
+import { makeStartVat, makeBringOutYourDead } from './util.js';
+import { makeMockGC } from './mock-gc.js';
+
+// virtual/durable collections serialize their keyShape/valueShape,
+// any Remotables therein must be compatible, and we should have
+// refcounts on them
+
+const shapetest = test.macro(async (t, collectionType, remotableType) => {
+  const { syscall, fakestore } = buildSyscall();
+  const gcTools = makeMockGC();
+  let remotable;
+  let map;
+
+  function buildRootObject(vatPowers) {
+    const { VatData } = vatPowers;
+    const initData = () => ({});
+    const handle = VatData.makeKindHandle('thing');
+    const makeVirtualThing = VatData.defineKind('thing', initData, {});
+    const makeDurableThing = VatData.defineDurableKind(handle, initData, {});
+    switch (remotableType) {
+      case 'ephemeral':
+        remotable = Far('thing', {});
+        break;
+      case 'virtual':
+        remotable = makeVirtualThing();
+        break;
+      case 'durable':
+        remotable = makeDurableThing();
+        break;
+      default:
+        throw Error(`unhandled ${remotableType}`);
+    }
+    t.truthy(remotable);
+    const valueShape = remotable;
+    const durable = collectionType === 'durable';
+    map = VatData.makeScalarBigMapStore('map', { valueShape, durable });
+    return Far('root', {});
+  }
+
+  const makeNS = () => ({ buildRootObject });
+  const ls = makeLiveSlots(syscall, 'vatA', {}, {}, gcTools, undefined, makeNS);
+  const { dispatch, testHooks } = ls;
+  const startVat = makeStartVat(kser());
+  if (collectionType === 'durable' && remotableType !== 'durable') {
+    await t.throwsAsync(() => dispatch(startVat), {
+      message: /value is not durable/,
+    });
+    // TODO: unhandled rejection interferes with the test
+    return;
+  }
+  await dispatch(startVat);
+
+  // the object we used in the valueShape schema ..
+  const vref = testHooks.valToSlot.get(remotable);
+  t.truthy(vref);
+
+  // .. should appear in the serialized schema
+  const mapVref = testHooks.valToSlot.get(map);
+  const collectionID = parseVatSlot(mapVref).subid;
+  const schemaKey = `vc.${collectionID}.|schemata`;
+  const schemataData = JSON.parse(fakestore.get(schemaKey));
+  t.deepEqual(schemataData.slots, [vref]);
+
+  // and it should hold a refcount
+  t.is(testHooks.getReachableRefCount(vref), 1);
+
+  // now pretend the collection is deleted, and do a BOYD
+  gcTools.kill(map);
+  gcTools.flushAllFRs();
+  await dispatch(makeBringOutYourDead());
+  // the refcount should be gone
+  t.falsy(testHooks.getReachableRefCount(vref));
+  // so should the schema (and all other keys)
+  t.falsy(fakestore.has(schemaKey));
+});
+
+test(
+  'virtual collection shape holds ephmeral',
+  shapetest,
+  'virtual',
+  'ephemeral',
+);
+test('virtual collection shape holds virtual', shapetest, 'virtual', 'virtual');
+test('virtual collection shape holds durable', shapetest, 'virtual', 'durable');
+
+test.skip(
+  'durable collection shape holds ephmeral',
+  shapetest,
+  'durable',
+  'ephemeral',
+);
+test.skip(
+  'durable collection shape holds virtual',
+  shapetest,
+  'durable',
+  'virtual',
+);
+test('durable collection shape holds durable', shapetest, 'durable', 'durable');
diff --git a/packages/swingset-liveslots/test/test-collection-upgrade.js b/packages/swingset-liveslots/test/test-collection-upgrade.js
new file mode 100644
index 00000000000..25c5d52a15e
--- /dev/null
+++ b/packages/swingset-liveslots/test/test-collection-upgrade.js
@@ -0,0 +1,135 @@
+/* eslint-disable no-await-in-loop, @jessie.js/no-nested-await, no-shadow */
+import test from 'ava';
+import '@endo/init/debug.js';
+
+import { Far } from '@endo/marshal';
+import { M } from '@agoric/store';
+import { makeLiveSlots } from '../src/liveslots.js';
+import { parseVatSlot } from '../src/parseVatSlots.js';
+import { kser } from './kmarshal.js';
+import { buildSyscall } from './liveslots-helpers.js';
+import { makeStartVat } from './util.js';
+import { makeMockGC } from './mock-gc.js';
+
+test('durable collections survive upgrade', async t => {
+  let map1;
+  let set1;
+  let thing1;
+  let thing2;
+  let thing3;
+
+  function build1(vatPowers, _vatParameters, baggage) {
+    const { VatData } = vatPowers;
+    const handle = VatData.makeKindHandle('thing');
+    baggage.init('handle', handle);
+    const initData = name => ({ name });
+    const how = { name: ({ state }) => state.name };
+    const makeDurableThing = VatData.defineDurableKind(handle, initData, how);
+    thing1 = makeDurableThing('thing1');
+    thing2 = makeDurableThing('thing2');
+    thing3 = makeDurableThing('thing3');
+    const valueShape = [thing1, M.any()];
+    const durable = true;
+    map1 = VatData.makeScalarBigMapStore('map', { valueShape, durable });
+    baggage.init('map', map1);
+    map1.init('string', harden([thing1, 'string']));
+    map1.init('number', harden([thing1, 123]));
+    map1.init('thing2', harden([thing1, thing2]));
+    // thing3 is only used as the valueShape
+    set1 = VatData.makeScalarBigSetStore('set', {
+      valueShape: thing3,
+      durable,
+    });
+    baggage.init('set', set1);
+    return Far('root', {});
+  }
+  const make1 = () => ({ buildRootObject: build1 });
+
+  const kvStore = new Map();
+  const { syscall: sc1 } = buildSyscall({ kvStore });
+  const gcTools1 = makeMockGC();
+  const ls1 = makeLiveSlots(sc1, 'vatA', {}, {}, gcTools1, undefined, make1);
+
+  const startVat = makeStartVat(kser());
+  await ls1.dispatch(startVat);
+
+  const mapVref = ls1.testHooks.valToSlot.get(map1);
+  const setVref = ls1.testHooks.valToSlot.get(set1);
+  const thing1Vref = ls1.testHooks.valToSlot.get(thing1);
+  const thing2Vref = ls1.testHooks.valToSlot.get(thing2);
+  const thing3Vref = ls1.testHooks.valToSlot.get(thing3);
+
+  // console.log(`-- map=${mapVref}, thing1=${thing1Vref}, thing2=${thing2Vref}`);
+
+  // map and set should have refcount 1, from baggage
+  t.is(ls1.testHooks.getReachableRefCount(mapVref), 1);
+  t.is(ls1.testHooks.getReachableRefCount(setVref), 1);
+  // thing1 should have a refcount of 4: one for valueShape, plus one
+  // for each entry
+  t.is(ls1.testHooks.getReachableRefCount(thing1Vref), 4);
+  // thing2 should have 1, only the 'thing2' entry
+  t.is(ls1.testHooks.getReachableRefCount(thing2Vref), 1);
+  // thing3 should have 1, just the Set's valueShape
+  t.is(ls1.testHooks.getReachableRefCount(thing3Vref), 1);
+
+  const collectionID = parseVatSlot(mapVref).subid;
+  const schemaKey = `vc.${collectionID}.|schemata`;
+  const schemataData = JSON.parse(kvStore.get(schemaKey));
+  t.deepEqual(schemataData.slots, [thing1Vref]);
+
+  // const compareEntriesByKey = ([ka], [kb]) => (ka < kb ? -1 : 1);
+  // t.log(Object.fromEntries([...kvStore.entries()].sort(compareEntriesByKey)));
+
+  // Simulate upgrade by starting from the non-empty kvStore.
+  const clonedStore = new Map(kvStore);
+
+  let map2;
+  let set2;
+  let newThing1;
+  let newThing2;
+
+  function build2(vatPowers, _vatParameters, baggage) {
+    const { VatData } = vatPowers;
+    const handle = baggage.get('handle');
+    const initData = name => ({ name });
+    const how = { name: ({ state }) => state.name };
+    VatData.defineDurableKind(handle, initData, how);
+    map2 = baggage.get('map');
+    let s;
+    [newThing1, s] = map2.get('string');
+    t.is(newThing1.name(), 'thing1');
+    t.is(s, 'string');
+    t.deepEqual(map2.get('string'), [newThing1, 'string']);
+    t.deepEqual(map2.get('number'), [newThing1, 123]);
+    newThing2 = map2.get('thing2')[1];
+    t.is(newThing2.name(), 'thing2');
+    set2 = baggage.get('set');
+    return Far('root', {});
+  }
+  const make2 = () => ({ buildRootObject: build2 });
+
+  const { syscall: sc2 } = buildSyscall({ kvStore: clonedStore });
+  const gcTools2 = makeMockGC();
+  const ls2 = makeLiveSlots(sc2, 'vatA', {}, {}, gcTools2, undefined, make2);
+
+  // restarting should work. this exercises valueShape being durable
+  // and being retrievable
+  await ls2.dispatch(startVat);
+
+  // [...ls2.testHooks.slotToVal.entries()].map(([slot,wr]) => console.log(slot, wr.deref()));
+
+  t.is(ls2.testHooks.slotToVal.get(thing1Vref).deref(), newThing1);
+
+  // the vrefs should all still be the same
+  t.is(ls2.testHooks.valToSlot.get(map2), mapVref);
+  t.is(ls2.testHooks.valToSlot.get(set2), setVref);
+  t.is(ls2.testHooks.valToSlot.get(newThing1), thing1Vref);
+  t.is(ls2.testHooks.valToSlot.get(newThing2), thing2Vref);
+
+  // refcounts should be the same
+  t.is(ls2.testHooks.getReachableRefCount(mapVref), 1);
+  t.is(ls1.testHooks.getReachableRefCount(setVref), 1);
+  t.is(ls2.testHooks.getReachableRefCount(thing1Vref), 4);
+  t.is(ls2.testHooks.getReachableRefCount(thing2Vref), 1);
+  t.is(ls2.testHooks.getReachableRefCount(thing3Vref), 1);
+});