diff --git a/internal/core/eval/closed.go b/internal/core/eval/closed.go
index fcfa52a..0b8025e 100644
--- a/internal/core/eval/closed.go
+++ b/internal/core/eval/closed.go
@@ -289,6 +289,8 @@
 // "and" semantics of conjunctions. It generates an error if a field is not
 // allowed.
 func (n *acceptor) verifyArcAllowed(ctx *adt.OpContext, f adt.Feature) *adt.Bottom {
+	// TODO(perf): this will also generate a message for f == 0. Do something
+	// more clever and only generate this when it is a user error.
 	filter := f.IsString() || f == adt.InvalidLabel
 	if filter && !n.verifyArcRecursive(ctx, n.tree, f) {
 		label := f.SelectorString(ctx)
diff --git a/internal/core/eval/eval.go b/internal/core/eval/eval.go
index 2121e42..82dba9a 100644
--- a/internal/core/eval/eval.go
+++ b/internal/core/eval/eval.go
@@ -153,6 +153,15 @@
 			// information than incorrect information.
 			for _, d := range d.Values {
 				d.Conjuncts = nil
+				for _, a := range d.Arcs {
+					for _, x := range a.Conjuncts {
+						// All the environments for embedded structs need to be
+						// dereferenced.
+						for env := x.Env; env != nil && env.Vertex == v; env = env.Up {
+							env.Vertex = d
+						}
+					}
+				}
 			}
 		}
 
@@ -251,13 +260,28 @@
 
 	case d != nil && len(d.Values) > 0:
 		v.Value = d
-		v.Arcs = nil
-		v.Structs = nil
 		// The conjuncts will have too much information. Better have no
 		// information than incorrect information.
 		for _, d := range d.Values {
+			// We clear the conjuncts for now. As these disjuncts are for API
+			// use only, we will fill them out when necessary (using Defaults).
 			d.Conjuncts = nil
+
+			// TODO: use a more principled form of dereferencing. For instance,
+			// disjuncts could already be assumed to be the given Vertex, and
+			// the the main vertex could be dereferenced during evaluation.
+			for _, a := range d.Arcs {
+				for _, x := range a.Conjuncts {
+					// All the environments for embedded structs need to be
+					// dereferenced.
+					for env := x.Env; env != nil && env.Vertex == v; env = env.Up {
+						env.Vertex = d
+					}
+				}
+			}
 		}
+		v.Arcs = nil
+		// v.Structs = nil // TODO: should we keep or discard the Structs?
 
 	default:
 		if r := n.result(); r.Value != nil {