diff --git a/src/cmd/compile/internal/types2/builtins.go b/src/cmd/compile/internal/types2/builtins.go
index 1779e32c5c..20c4ff62a1 100644
--- a/src/cmd/compile/internal/types2/builtins.go
+++ b/src/cmd/compile/internal/types2/builtins.go
@@ -749,14 +749,12 @@ func (check *Checker) applyTypeFunc(f func(Type) Type, x Type) Type {
 	if tp := asTypeParam(x); tp != nil {
 		// Test if t satisfies the requirements for the argument
 		// type and collect possible result types at the same time.
-		// TODO(gri) This needs to consider the ~ information if we
-		//           have a union type.
 		var rtypes []Type
-		var tilde []bool
-		if !tp.Bound().is(func(x Type) bool {
-			if r := f(x); r != nil {
+		var tildes []bool
+		if !tp.Bound().is(func(typ Type, tilde bool) bool {
+			if r := f(typ); r != nil {
 				rtypes = append(rtypes, r)
-				tilde = append(tilde, true) // for now - see TODO above
+				tildes = append(tildes, tilde)
 				return true
 			}
 			return false
@@ -772,7 +770,7 @@ func (check *Checker) applyTypeFunc(f func(Type) Type, x Type) Type {
 		// construct a suitable new type parameter
 		tpar := NewTypeName(nopos, nil /* = Universe pkg */, "<type parameter>", nil)
 		ptyp := check.NewTypeParam(tpar, 0, &emptyInterface) // assigns type to tpar as a side-effect
-		tsum := newUnion(rtypes, tilde)
+		tsum := newUnion(rtypes, tildes)
 		ptyp.bound = &Interface{allMethods: markComplete, allTypes: tsum}
 
 		return ptyp
diff --git a/src/cmd/compile/internal/types2/infer.go b/src/cmd/compile/internal/types2/infer.go
index 73ea8330d4..63cd63aacc 100644
--- a/src/cmd/compile/internal/types2/infer.go
+++ b/src/cmd/compile/internal/types2/infer.go
@@ -328,7 +328,7 @@ func (w *tpWalker) isParameterized(typ Type) (res bool) {
 					return true
 				}
 			}
-			return w.isParameterizedList(unpack(t.allTypes))
+			return w.isParameterized(t.allTypes)
 		}
 
 		return t.iterate(func(t *Interface) bool {
@@ -477,11 +477,14 @@ func (check *Checker) inferB(tparams []*TypeName, targs []Type, report bool) (ty
 func (check *Checker) structuralType(constraint Type) Type {
 	if iface, _ := under(constraint).(*Interface); iface != nil {
 		check.completeInterface(nopos, iface)
-		types := unpack(iface.allTypes)
-		if len(types) == 1 {
-			return types[0]
+		if u, _ := iface.allTypes.(*Union); u != nil {
+			if u.NumTerms() == 1 {
+				// TODO(gri) do we need to respect tilde?
+				return u.types[0]
+			}
+			return nil
 		}
-		return nil
+		return iface.allTypes
 	}
-	return constraint
+	return nil
 }
diff --git a/src/cmd/compile/internal/types2/subst.go b/src/cmd/compile/internal/types2/subst.go
index 617a03ddbc..35ca197d64 100644
--- a/src/cmd/compile/internal/types2/subst.go
+++ b/src/cmd/compile/internal/types2/subst.go
@@ -194,14 +194,15 @@ func (check *Checker) satisfies(pos syntax.Pos, targ Type, tpar *TypeParam, smap
 			check.softErrorf(pos, "%s does not satisfy %s (%s has no type constraints)", targ, tpar.bound, targ)
 			return false
 		}
-		for _, t := range unpack(targBound.allTypes) {
-			if !iface.isSatisfiedBy(t) {
+		return iface.is(func(typ Type, tilde bool) bool {
+			// TODO(gri) incorporate tilde information!
+			if !iface.isSatisfiedBy(typ) {
 				// TODO(gri) match this error message with the one below (or vice versa)
-				check.softErrorf(pos, "%s does not satisfy %s (%s type constraint %s not found in %s)", targ, tpar.bound, targ, t, iface.allTypes)
+				check.softErrorf(pos, "%s does not satisfy %s (%s type constraint %s not found in %s)", targ, tpar.bound, targ, typ, iface.allTypes)
 				return false
 			}
-		}
-		return false
+			return true
+		})
 	}
 
 	// Otherwise, targ's type or underlying type must also be one of the interface types listed, if any.
diff --git a/src/cmd/compile/internal/types2/type.go b/src/cmd/compile/internal/types2/type.go
index 990b9d374c..92f35f1279 100644
--- a/src/cmd/compile/internal/types2/type.go
+++ b/src/cmd/compile/internal/types2/type.go
@@ -272,29 +272,17 @@ type Interface struct {
 	obj Object // type declaration defining this interface; or nil (for better error messages)
 }
 
-// unpack unpacks a type into a list of types.
-// TODO(gri) Try to eliminate the need for this function.
-func unpack(typ Type) []Type {
-	if typ == nil {
-		return nil
-	}
-	if u := asUnion(typ); u != nil {
-		return u.types
-	}
-	return []Type{typ}
-}
-
-// is reports whether interface t represents types that all satisfy pred.
-func (t *Interface) is(pred func(Type) bool) bool {
-	if t.allTypes == nil {
+// is reports whether interface t represents types that all satisfy f.
+func (t *Interface) is(f func(Type, bool) bool) bool {
+	switch t := t.allTypes.(type) {
+	case nil, *top:
+		// TODO(gri) should settle on top or nil to represent this case
 		return false // we must have at least one type! (was bug)
+	case *Union:
+		return t.is(func(typ Type, tilde bool) bool { return f(typ, tilde) })
+	default:
+		return f(t, false)
 	}
-	for _, t := range unpack(t.allTypes) {
-		if !pred(t) {
-			return false
-		}
-	}
-	return true
 }
 
 // emptyInterface represents the empty (completed) interface
@@ -828,11 +816,6 @@ func asSignature(t Type) *Signature {
 	return op
 }
 
-func asUnion(t Type) *Union {
-	op, _ := optype(t).(*Union)
-	return op
-}
-
 func asInterface(t Type) *Interface {
 	op, _ := optype(t).(*Interface)
 	return op