diff --git a/cue/testdata/fulleval/035_optionals_with_label_filters.txtar b/cue/testdata/fulleval/035_optionals_with_label_filters.txtar
index 9204d37..e9c1cf8 100644
--- a/cue/testdata/fulleval/035_optionals_with_label_filters.txtar
+++ b/cue/testdata/fulleval/035_optionals_with_label_filters.txtar
@@ -113,10 +113,6 @@
     ./in.cue:9:2
     ./in.cue:22:8
     ./in.cue:23:8
-jobs3.fooTest1: field `cmd` not allowed:
-    ./in.cue:2:7
-    ./in.cue:6:8
-    ./in.cue:23:18
 jobs2.fooTest.name: invalid value "badName" (out of bound =~"^test"):
     ./in.cue:9:22
 
@@ -162,11 +158,7 @@
     //     ./in.cue:9:2
     //     ./in.cue:22:8
     //     ./in.cue:23:8
-    fooTest1: (_|_){
-      // [eval] jobs3.fooTest1: field `cmd` not allowed:
-      //     ./in.cue:2:7
-      //     ./in.cue:6:8
-      //     ./in.cue:23:18
+    fooTest1: (#struct){
       name: (string){ "badName" }
       cmd: (string){ string }
     }
diff --git a/cue/testdata/resolve/035_excluded_embedding_from_closing.txtar b/cue/testdata/resolve/035_excluded_embedding_from_closing.txtar
index e719e07..ebd92c4 100644
--- a/cue/testdata/resolve/035_excluded_embedding_from_closing.txtar
+++ b/cue/testdata/resolve/035_excluded_embedding_from_closing.txtar
@@ -65,7 +65,6 @@
 -- out/eval --
 Errors:
 V.b: field `extra` not allowed:
-    ./in.cue:1:5
     ./in.cue:6:10
     ./in.cue:11:5
 V.c: field `e` not allowed:
@@ -102,7 +101,6 @@
     }
     b: (_|_){
       // [eval] V.b: field `extra` not allowed:
-      //     ./in.cue:1:5
       //     ./in.cue:6:10
       //     ./in.cue:11:5
       open: (int){ int }
diff --git a/internal/ci/workflows.cue b/internal/ci/workflows.cue
index 6d2d564..1a5c1a5 100644
--- a/internal/ci/workflows.cue
+++ b/internal/ci/workflows.cue
@@ -7,7 +7,7 @@
 
 workflowsDir: *"./" | string @tag(workflowsDir)
 
-workflows: [...{file: string, schema: json.#Workflow}]
+workflows: [...{file: string, schema: (json.#Workflow&{})}]
 workflows: [
 	{
 		file:   "test.yml"
@@ -29,7 +29,7 @@
 
 // TODO: drop when cuelang.org/issue/390 is fixed.
 // Declare definitions for sub-schemas
-#job:  (json.#Workflow.jobs & {x: _}).x
+#job:  ((json.#Workflow & {}).jobs & {x: _}).x
 #step: ((#job & {steps:           _}).steps & [_])[0]
 
 #latestGo: "1.14.3"
diff --git a/internal/core/eval/closed.go b/internal/core/eval/closed.go
index 5c9ae62..56a0d7f 100644
--- a/internal/core/eval/closed.go
+++ b/internal/core/eval/closed.go
@@ -162,11 +162,19 @@
 // of this flat list.
 //
 func updateClosed(c *CloseDef, replace map[uint32]*CloseDef) *CloseDef { // used in eval.go
+	// Insert an entry for CloseID 0 if we are about to replace it. By default
+	// 0, which is the majority case, is omitted.
+	if c != nil && replace[0] != nil && !containsClosed(c, 0) {
+		c = &CloseDef{IsAnd: true, List: []*CloseDef{c, {}}}
+	}
+
 	switch {
 	case c == nil:
 		and := []*CloseDef{}
 		for _, c := range replace {
-			and = append(and, c)
+			if c != nil {
+				and = append(and, c)
+			}
 		}
 		switch len(and) {
 		case 0:
@@ -190,11 +198,17 @@
 	// If c is a leaf or AND node, replace it outright. If both are an OR node,
 	// merge the lists.
 	if len(c.List) == 0 || !c.IsAnd {
-		if sub := replace[c.ID]; sub != nil {
+		switch sub, ok := replace[c.ID]; {
+		case sub != nil:
 			if isOr(sub) && isOr(c) {
 				sub.List = append(sub.List, c.List...)
 			}
 			return sub
+
+		case !ok:
+			if len(c.List) == 0 {
+				return nil // drop from list
+			}
 		}
 	}
 
@@ -213,11 +227,14 @@
 		return c
 	}
 
-	if k == 1 {
+	switch k {
+	case 0:
+		return nil
+	case 1:
 		return buf[0]
+	default:
+		return &CloseDef{Src: c.Src, ID: c.ID, IsAnd: c.IsAnd, List: buf[:k]}
 	}
-
-	return &CloseDef{Src: c.Src, ID: c.ID, IsAnd: c.IsAnd, List: buf[:k]}
 }
 
 // UpdateReplace is called after evaluating a conjunct at the top of the arc
@@ -387,3 +404,17 @@
 		collectPositions(ctx, x)
 	}
 }
+
+// containsClosed reports whether c contains any CloseDef with ID x,
+// recursively.
+func containsClosed(c *CloseDef, x uint32) bool {
+	if c.ID == x && !c.IsAnd {
+		return true
+	}
+	for _, e := range c.List {
+		if containsClosed(e, x) {
+			return true
+		}
+	}
+	return false
+}
diff --git a/internal/core/eval/closed_test.go b/internal/core/eval/closed_test.go
index 144ecce..c0ed278 100644
--- a/internal/core/eval/closed_test.go
+++ b/internal/core/eval/closed_test.go
@@ -27,6 +27,28 @@
 		replace map[uint32]*CloseDef
 		want    *CloseDef
 	}{{
+		desc:  "introduce new",
+		close: nil,
+		replace: map[uint32]*CloseDef{
+			0: {ID: 2, IsAnd: false, List: nil},
+		},
+		want: &CloseDef{
+			ID: 0x02,
+		},
+	}, {
+		desc: "auto insert missing 0",
+		close: &CloseDef{
+			ID: 1,
+		},
+		replace: map[uint32]*CloseDef{
+			0: {ID: 2, IsAnd: false, List: nil},
+			1: nil, // keep 1
+		},
+		want: &CloseDef{
+			IsAnd: true,
+			List:  []*CloseDef{{ID: 1}, {ID: 2}},
+		},
+	}, {
 		desc: "a: #A & #B",
 		close: &CloseDef{
 			ID: 1,
@@ -40,18 +62,38 @@
 			List:  []*CloseDef{{ID: 2}, {ID: 3}},
 		},
 	}, {
+		desc: "eliminateUnusedToEmpty",
+		close: &CloseDef{
+			ID: 1,
+		},
+		replace: map[uint32]*CloseDef{
+			0: nil,
+		},
+		want: nil,
+	}, {
 		// Eliminate an embedding for which there are no more entries.
-		// 	desc: "eliminateOneEmbedding",
-		// 	close: &CloseDef{
-		// 		ID: 0,
-		// 		List: []*CloseDef{
-		// 			{ID: 2},
-		// 			{ID: 3},
-		// 		},
-		// 	},
-		// 	replace: map[uint32]*CloseDef{2: nil},
-		// 	want:    &CloseDef{ID: 2},
-		// }, {
+		desc: "eliminateOneEmbedding",
+		close: &CloseDef{
+			ID: 0,
+			List: []*CloseDef{
+				{ID: 2},
+				{ID: 3},
+			},
+		},
+		replace: map[uint32]*CloseDef{2: nil},
+		want:    &CloseDef{ID: 2},
+	}, {
+		desc: "eliminateAllEmbeddings",
+		close: &CloseDef{
+			ID: 2,
+			List: []*CloseDef{
+				{ID: 2},
+				{ID: 3},
+			},
+		},
+		replace: map[uint32]*CloseDef{0: {ID: 4}, 4: nil},
+		want:    &CloseDef{ID: 4},
+	}, {
 		// Do not eliminate an embedding that has a replacement.
 		desc: "eliminateOneEmbeddingByMultiple",
 		close: &CloseDef{
diff --git a/internal/core/eval/eval.go b/internal/core/eval/eval.go
index 896c983..8b58c7e 100644
--- a/internal/core/eval/eval.go
+++ b/internal/core/eval/eval.go
@@ -570,7 +570,28 @@
 		n.needClose = n.needClose || a.isClosed
 	}
 
-	updated := updateClosed(c, n.replace)
+	replace := n.replace
+	if replace == nil {
+		replace = map[uint32]*CloseDef{}
+	}
+
+	// Mark any used CloseID to keep, if not already replaced.
+	for _, x := range n.optionals {
+		if _, ok := replace[x.env.CloseID]; !ok {
+			replace[x.env.CloseID] = nil
+		}
+	}
+	for _, a := range n.node.Arcs {
+		for _, c := range a.Conjuncts {
+			if c.Env != nil {
+				if _, ok := replace[c.Env.CloseID]; !ok {
+					replace[c.Env.CloseID] = nil
+				}
+			}
+		}
+	}
+
+	updated := updateClosed(c, replace)
 	if updated == nil && n.needClose {
 		updated = &CloseDef{Src: n.node}
 	}
@@ -1044,7 +1065,7 @@
 		// values on which they depend fail.
 		ctx.Unify(ctx, arc, adt.Finalized)
 
-		if arc.Label.IsDef() {
+		if arc.Label.IsDef() { // should test whether closed, not isDef?
 			id := n.eval.nextID()
 			n.insertClosed(arc, id, cyclic, arc)
 		} else {