diff --git a/src/go/types/builtins.go b/src/go/types/builtins.go
index fb660b5cc8..af374b70c6 100644
--- a/src/go/types/builtins.go
+++ b/src/go/types/builtins.go
@@ -257,7 +257,7 @@ func (check *Checker) builtin(x *operand, call *ast.CallExpr, id builtinId) (_ b
 		}
 
 		// both argument types must be identical
-		if !Identical(x.typ, y.typ) {
+		if !check.identical(x.typ, y.typ) {
 			check.invalidArg(x.pos(), "mismatched types %s and %s", x.typ, y.typ)
 			return
 		}
@@ -322,7 +322,7 @@ func (check *Checker) builtin(x *operand, call *ast.CallExpr, id builtinId) (_ b
 			return
 		}
 
-		if !Identical(dst, src) {
+		if !check.identical(dst, src) {
 			check.invalidArg(x.pos(), "arguments to copy %s and %s have different element types %s and %s", x, &y, dst, src)
 			return
 		}
diff --git a/src/go/types/call.go b/src/go/types/call.go
index 1400e0f00b..31f9372644 100644
--- a/src/go/types/call.go
+++ b/src/go/types/call.go
@@ -464,6 +464,11 @@ func (check *Checker) selector(x *operand, e *ast.SelectorExpr) {
 				if m := mset.Lookup(check.pkg, sel); m == nil || m.obj != obj {
 					check.dump("%v: (%s).%v -> %s", e.Pos(), typ, obj.name, m)
 					check.dump("%s\n", mset)
+					// Caution: MethodSets are supposed to be used externally
+					// only (after all interface types were completed). It's
+					// now possible that we get here incorrectly. Not urgent
+					// to fix since we only run this code in debug mode.
+					// TODO(gri) fix this eventually.
 					panic("method sets and lookup don't agree")
 				}
 			}
diff --git a/src/go/types/conversions.go b/src/go/types/conversions.go
index fecb7b617f..7ea8fd70aa 100644
--- a/src/go/types/conversions.go
+++ b/src/go/types/conversions.go
@@ -89,7 +89,7 @@ func (x *operand) convertibleTo(check *Checker, T Type) bool {
 	V := x.typ
 	Vu := V.Underlying()
 	Tu := T.Underlying()
-	if IdenticalIgnoreTags(Vu, Tu) {
+	if check.identicalIgnoreTags(Vu, Tu) {
 		return true
 	}
 
@@ -97,7 +97,7 @@ func (x *operand) convertibleTo(check *Checker, T Type) bool {
 	// have identical underlying types if tags are ignored"
 	if V, ok := V.(*Pointer); ok {
 		if T, ok := T.(*Pointer); ok {
-			if IdenticalIgnoreTags(V.base.Underlying(), T.base.Underlying()) {
+			if check.identicalIgnoreTags(V.base.Underlying(), T.base.Underlying()) {
 				return true
 			}
 		}
diff --git a/src/go/types/expr.go b/src/go/types/expr.go
index 66d62d6885..0edd2789fb 100644
--- a/src/go/types/expr.go
+++ b/src/go/types/expr.go
@@ -548,9 +548,6 @@ func (check *Checker) convertUntyped(x *operand, target Type) {
 			}
 		}
 	case *Interface:
-		if !x.isNil() && !t.Empty() /* empty interfaces are ok */ {
-			goto Error
-		}
 		// Update operand types to the default type rather then
 		// the target (interface) type: values must have concrete
 		// dynamic types. If the value is nil, keep it untyped
@@ -561,6 +558,7 @@ func (check *Checker) convertUntyped(x *operand, target Type) {
 			target = Typ[UntypedNil]
 		} else {
 			// cannot assign untyped values to non-empty interfaces
+			check.completeInterface(t)
 			if !t.Empty() {
 				goto Error
 			}
@@ -809,7 +807,7 @@ func (check *Checker) binary(x *operand, e *ast.BinaryExpr, lhs, rhs ast.Expr, o
 		return
 	}
 
-	if !Identical(x.typ, y.typ) {
+	if !check.identical(x.typ, y.typ) {
 		// only report an error if we have valid types
 		// (otherwise we had an error reported elsewhere already)
 		if x.typ != Typ[Invalid] && y.typ != Typ[Invalid] {
@@ -1223,7 +1221,7 @@ func (check *Checker) exprInternal(x *operand, e ast.Expr, hint Type) exprKind {
 					xkey := keyVal(x.val)
 					if _, ok := utyp.key.Underlying().(*Interface); ok {
 						for _, vtyp := range visited[xkey] {
-							if Identical(vtyp, x.typ) {
+							if check.identical(vtyp, x.typ) {
 								duplicate = true
 								break
 							}
diff --git a/src/go/types/issues_test.go b/src/go/types/issues_test.go
index c9f5413920..1d0c0cb08a 100644
--- a/src/go/types/issues_test.go
+++ b/src/go/types/issues_test.go
@@ -465,3 +465,31 @@ func TestIssue29029(t *testing.T) {
 		t.Errorf("\ngot : %swant: %s", got, want)
 	}
 }
+
+func TestIssue34151(t *testing.T) {
+	const asrc = `package a; type I interface{ M() }; type T struct { F interface { I } }`
+	const bsrc = `package b; import "a"; type T struct { F interface { a.I } }; var _ = a.T(T{})`
+
+	a, err := pkgFor("a", asrc, nil)
+	if err != nil {
+		t.Fatalf("package %s failed to typecheck: %v", a.Name(), err)
+	}
+
+	bast := mustParse(t, bsrc)
+	conf := Config{Importer: importHelper{a}}
+	b, err := conf.Check(bast.Name.Name, fset, []*ast.File{bast}, nil)
+	if err != nil {
+		t.Errorf("package %s failed to typecheck: %v", b.Name(), err)
+	}
+}
+
+type importHelper struct {
+	pkg *Package
+}
+
+func (h importHelper) Import(path string) (*Package, error) {
+	if path != h.pkg.Path() {
+		return nil, fmt.Errorf("got package path %q; want %q", path, h.pkg.Path())
+	}
+	return h.pkg, nil
+}
diff --git a/src/go/types/lookup.go b/src/go/types/lookup.go
index 265e30971d..648e100060 100644
--- a/src/go/types/lookup.go
+++ b/src/go/types/lookup.go
@@ -200,7 +200,7 @@ func (check *Checker) lookupFieldOrMethod(T Type, addressable bool, pkg *Package
 			return
 		}
 
-		current = consolidateMultiples(next)
+		current = check.consolidateMultiples(next)
 	}
 
 	return nil, nil, false // not found
@@ -217,7 +217,7 @@ type embeddedType struct {
 // consolidateMultiples collects multiple list entries with the same type
 // into a single entry marked as containing multiples. The result is the
 // consolidated list.
-func consolidateMultiples(list []embeddedType) []embeddedType {
+func (check *Checker) consolidateMultiples(list []embeddedType) []embeddedType {
 	if len(list) <= 1 {
 		return list // at most one entry - nothing to do
 	}
@@ -225,7 +225,7 @@ func consolidateMultiples(list []embeddedType) []embeddedType {
 	n := 0                     // number of entries w/ unique type
 	prev := make(map[Type]int) // index at which type was previously seen
 	for _, e := range list {
-		if i, found := lookupType(prev, e.typ); found {
+		if i, found := check.lookupType(prev, e.typ); found {
 			list[i].multiples = true
 			// ignore this entry
 		} else {
@@ -237,14 +237,14 @@ func consolidateMultiples(list []embeddedType) []embeddedType {
 	return list[:n]
 }
 
-func lookupType(m map[Type]int, typ Type) (int, bool) {
+func (check *Checker) lookupType(m map[Type]int, typ Type) (int, bool) {
 	// fast path: maybe the types are equal
 	if i, found := m[typ]; found {
 		return i, true
 	}
 
 	for t, i := range m {
-		if Identical(t, typ) {
+		if check.identical(t, typ) {
 			return i, true
 		}
 	}
@@ -278,8 +278,6 @@ func (check *Checker) missingMethod(V Type, T *Interface, static bool) (method *
 		return
 	}
 
-	// TODO(gri) Consider using method sets here. Might be more efficient.
-
 	if ityp, _ := V.Underlying().(*Interface); ityp != nil {
 		check.completeInterface(ityp)
 		// TODO(gri) allMethods is sorted - can do this more efficiently
@@ -290,7 +288,7 @@ func (check *Checker) missingMethod(V Type, T *Interface, static bool) (method *
 				if static {
 					return m, false
 				}
-			case !Identical(obj.Type(), m.typ):
+			case !check.identical(obj.Type(), m.typ):
 				return m, true
 			}
 		}
@@ -312,7 +310,7 @@ func (check *Checker) missingMethod(V Type, T *Interface, static bool) (method *
 			check.objDecl(f, nil)
 		}
 
-		if !Identical(f.typ, m.typ) {
+		if !check.identical(f.typ, m.typ) {
 			return m, true
 		}
 	}
diff --git a/src/go/types/methodset.go b/src/go/types/methodset.go
index 1c2208002e..a236fe2ea8 100644
--- a/src/go/types/methodset.go
+++ b/src/go/types/methodset.go
@@ -180,7 +180,12 @@ func NewMethodSet(T Type) *MethodSet {
 			}
 		}
 
-		current = consolidateMultiples(next)
+		// It's ok to call consolidateMultiples with a nil *Checker because
+		// MethodSets are not used internally (outside debug mode). When used
+		// externally, interfaces are expected to be completed and then we do
+		// not need a *Checker to complete them when (indirectly) calling
+		// Checker.identical via consolidateMultiples.
+		current = (*Checker)(nil).consolidateMultiples(next)
 	}
 
 	if len(base) == 0 {
diff --git a/src/go/types/operand.go b/src/go/types/operand.go
index 97ca6c622f..1259f44300 100644
--- a/src/go/types/operand.go
+++ b/src/go/types/operand.go
@@ -211,7 +211,7 @@ func (x *operand) assignableTo(check *Checker, T Type, reason *string) bool {
 	V := x.typ
 
 	// x's type is identical to T
-	if Identical(V, T) {
+	if check.identical(V, T) {
 		return true
 	}
 
@@ -236,6 +236,7 @@ func (x *operand) assignableTo(check *Checker, T Type, reason *string) bool {
 				return Vb.kind == UntypedBool && isBoolean(Tu)
 			}
 		case *Interface:
+			check.completeInterface(t)
 			return x.isNil() || t.Empty()
 		case *Pointer, *Signature, *Slice, *Map, *Chan:
 			return x.isNil()
@@ -245,7 +246,7 @@ func (x *operand) assignableTo(check *Checker, T Type, reason *string) bool {
 
 	// x's type V and T have identical underlying types
 	// and at least one of V or T is not a named type
-	if Identical(Vu, Tu) && (!isNamed(V) || !isNamed(T)) {
+	if check.identical(Vu, Tu) && (!isNamed(V) || !isNamed(T)) {
 		return true
 	}
 
@@ -268,7 +269,7 @@ func (x *operand) assignableTo(check *Checker, T Type, reason *string) bool {
 	// type, x's type V and T have identical element types,
 	// and at least one of V or T is not a named type
 	if Vc, ok := Vu.(*Chan); ok && Vc.dir == SendRecv {
-		if Tc, ok := Tu.(*Chan); ok && Identical(Vc.elem, Tc.elem) {
+		if Tc, ok := Tu.(*Chan); ok && check.identical(Vc.elem, Tc.elem) {
 			return !isNamed(V) || !isNamed(T)
 		}
 	}
diff --git a/src/go/types/predicates.go b/src/go/types/predicates.go
index 46ad4e2dc4..faaf753cd8 100644
--- a/src/go/types/predicates.go
+++ b/src/go/types/predicates.go
@@ -110,16 +110,31 @@ func hasNil(typ Type) bool {
 	return false
 }
 
+// The functions Identical and IdenticalIgnoreTags are
+// provided for external use only, after interface types
+// were fully set up (completed). During type-checking,
+// use the methods identical and identicalIgnoreTags
+// which take a non-nil *Checker receiver.
+// TODO(gri) factor these out into api.go.
+
 // Identical reports whether x and y are identical types.
 // Receivers of Signature types are ignored.
 func Identical(x, y Type) bool {
-	return identical(x, y, true, nil)
+	return (*Checker)(nil).identical(x, y)
+}
+
+func (check *Checker) identical(x, y Type) bool {
+	return check.identical0(x, y, true, nil)
 }
 
 // IdenticalIgnoreTags reports whether x and y are identical types if tags are ignored.
 // Receivers of Signature types are ignored.
 func IdenticalIgnoreTags(x, y Type) bool {
-	return identical(x, y, false, nil)
+	return (*Checker)(nil).identicalIgnoreTags(x, y)
+}
+
+func (check *Checker) identicalIgnoreTags(x, y Type) bool {
+	return check.identical0(x, y, false, nil)
 }
 
 // An ifacePair is a node in a stack of interface type pairs compared for identity.
@@ -132,7 +147,7 @@ func (p *ifacePair) identical(q *ifacePair) bool {
 	return p.x == q.x && p.y == q.y || p.x == q.y && p.y == q.x
 }
 
-func identical(x, y Type, cmpTags bool, p *ifacePair) bool {
+func (check *Checker) identical0(x, y Type, cmpTags bool, p *ifacePair) bool {
 	if x == y {
 		return true
 	}
@@ -152,13 +167,13 @@ func identical(x, y Type, cmpTags bool, p *ifacePair) bool {
 		if y, ok := y.(*Array); ok {
 			// If one or both array lengths are unknown (< 0) due to some error,
 			// assume they are the same to avoid spurious follow-on errors.
-			return (x.len < 0 || y.len < 0 || x.len == y.len) && identical(x.elem, y.elem, cmpTags, p)
+			return (x.len < 0 || y.len < 0 || x.len == y.len) && check.identical0(x.elem, y.elem, cmpTags, p)
 		}
 
 	case *Slice:
 		// Two slice types are identical if they have identical element types.
 		if y, ok := y.(*Slice); ok {
-			return identical(x.elem, y.elem, cmpTags, p)
+			return check.identical0(x.elem, y.elem, cmpTags, p)
 		}
 
 	case *Struct:
@@ -173,7 +188,7 @@ func identical(x, y Type, cmpTags bool, p *ifacePair) bool {
 					if f.embedded != g.embedded ||
 						cmpTags && x.Tag(i) != y.Tag(i) ||
 						!f.sameId(g.pkg, g.name) ||
-						!identical(f.typ, g.typ, cmpTags, p) {
+						!check.identical0(f.typ, g.typ, cmpTags, p) {
 						return false
 					}
 				}
@@ -184,7 +199,7 @@ func identical(x, y Type, cmpTags bool, p *ifacePair) bool {
 	case *Pointer:
 		// Two pointer types are identical if they have identical base types.
 		if y, ok := y.(*Pointer); ok {
-			return identical(x.base, y.base, cmpTags, p)
+			return check.identical0(x.base, y.base, cmpTags, p)
 		}
 
 	case *Tuple:
@@ -195,7 +210,7 @@ func identical(x, y Type, cmpTags bool, p *ifacePair) bool {
 				if x != nil {
 					for i, v := range x.vars {
 						w := y.vars[i]
-						if !identical(v.typ, w.typ, cmpTags, p) {
+						if !check.identical0(v.typ, w.typ, cmpTags, p) {
 							return false
 						}
 					}
@@ -211,8 +226,8 @@ func identical(x, y Type, cmpTags bool, p *ifacePair) bool {
 		// names are not required to match.
 		if y, ok := y.(*Signature); ok {
 			return x.variadic == y.variadic &&
-				identical(x.params, y.params, cmpTags, p) &&
-				identical(x.results, y.results, cmpTags, p)
+				check.identical0(x.params, y.params, cmpTags, p) &&
+				check.identical0(x.results, y.results, cmpTags, p)
 		}
 
 	case *Interface:
@@ -220,6 +235,14 @@ func identical(x, y Type, cmpTags bool, p *ifacePair) bool {
 		// the same names and identical function types. Lower-case method names from
 		// different packages are always different. The order of the methods is irrelevant.
 		if y, ok := y.(*Interface); ok {
+			// If identical0 is called (indirectly) via an external API entry point
+			// (such as Identical, IdenticalIgnoreTags, etc.), check is nil. But in
+			// that case, interfaces are expected to be complete and lazy completion
+			// here is not needed.
+			if check != nil {
+				check.completeInterface(x)
+				check.completeInterface(y)
+			}
 			a := x.allMethods
 			b := y.allMethods
 			if len(a) == len(b) {
@@ -258,7 +281,7 @@ func identical(x, y Type, cmpTags bool, p *ifacePair) bool {
 				}
 				for i, f := range a {
 					g := b[i]
-					if f.Id() != g.Id() || !identical(f.typ, g.typ, cmpTags, q) {
+					if f.Id() != g.Id() || !check.identical0(f.typ, g.typ, cmpTags, q) {
 						return false
 					}
 				}
@@ -269,14 +292,14 @@ func identical(x, y Type, cmpTags bool, p *ifacePair) bool {
 	case *Map:
 		// Two map types are identical if they have identical key and value types.
 		if y, ok := y.(*Map); ok {
-			return identical(x.key, y.key, cmpTags, p) && identical(x.elem, y.elem, cmpTags, p)
+			return check.identical0(x.key, y.key, cmpTags, p) && check.identical0(x.elem, y.elem, cmpTags, p)
 		}
 
 	case *Chan:
 		// Two channel types are identical if they have identical value types
 		// and the same direction.
 		if y, ok := y.(*Chan); ok {
-			return x.dir == y.dir && identical(x.elem, y.elem, cmpTags, p)
+			return x.dir == y.dir && check.identical0(x.elem, y.elem, cmpTags, p)
 		}
 
 	case *Named:
diff --git a/src/go/types/stdlib_test.go b/src/go/types/stdlib_test.go
index a3cbe95b3a..1b1db5d2dd 100644
--- a/src/go/types/stdlib_test.go
+++ b/src/go/types/stdlib_test.go
@@ -182,6 +182,7 @@ func TestStdFixed(t *testing.T) {
 		"issue20780.go",  // go/types does not have constraints on stack size
 		"issue31747.go",  // go/types does not have constraints on language level (-lang=go1.12) (see #31793)
 		"issue34329.go",  // go/types does not have constraints on language level (-lang=go1.13) (see #31793)
+		"bug251.go",      // issue #34333 which was exposed with fix for #34151
 	)
 }
 
diff --git a/src/go/types/stmt.go b/src/go/types/stmt.go
index abd9d05ef2..c1593bbee9 100644
--- a/src/go/types/stmt.go
+++ b/src/go/types/stmt.go
@@ -249,7 +249,7 @@ L:
 			// look for duplicate types for a given value
 			// (quadratic algorithm, but these lists tend to be very short)
 			for _, vt := range seen[val] {
-				if Identical(v.typ, vt.typ) {
+				if check.identical(v.typ, vt.typ) {
 					check.errorf(v.pos(), "duplicate case %s in expression switch", &v)
 					check.error(vt.pos, "\tprevious case") // secondary error, \t indented
 					continue L
@@ -270,7 +270,7 @@ L:
 		// look for duplicate types
 		// (quadratic algorithm, but type switches tend to be reasonably small)
 		for t, pos := range seen {
-			if T == nil && t == nil || T != nil && t != nil && Identical(T, t) {
+			if T == nil && t == nil || T != nil && t != nil && check.identical(T, t) {
 				// talk about "case" rather than "type" because of nil case
 				Ts := "nil"
 				if T != nil {
diff --git a/src/go/types/testdata/cycles2.src b/src/go/types/testdata/cycles2.src
index 98ca6f4e44..5fd9e838b6 100644
--- a/src/go/types/testdata/cycles2.src
+++ b/src/go/types/testdata/cycles2.src
@@ -58,7 +58,9 @@ var y interface {
 	A
 	B
 }
-var _ = x == y
+
+// TODO(gri) This should be a valid compare. See #33656.
+var _ = x /* ERROR cannot compare */ == y
 
 
 // Test case for issue 6638.
diff --git a/src/go/types/type.go b/src/go/types/type.go
index 5c28a2e7ba..6263da06f2 100644
--- a/src/go/types/type.go
+++ b/src/go/types/type.go
@@ -329,14 +329,23 @@ func (t *Interface) Embedded(i int) *Named { tname, _ := t.embeddeds[i].(*Named)
 func (t *Interface) EmbeddedType(i int) Type { return t.embeddeds[i] }
 
 // NumMethods returns the total number of methods of interface t.
-func (t *Interface) NumMethods() int { return len(t.allMethods) }
+// The interface must have been completed.
+func (t *Interface) NumMethods() int { t.assertCompleteness(); return len(t.allMethods) }
+
+func (t *Interface) assertCompleteness() {
+	if t.allMethods == nil {
+		panic("interface is incomplete")
+	}
+}
 
 // Method returns the i'th method of interface t for 0 <= i < t.NumMethods().
 // The methods are ordered by their unique Id.
-func (t *Interface) Method(i int) *Func { return t.allMethods[i] }
+// The interface must have been completed.
+func (t *Interface) Method(i int) *Func { t.assertCompleteness(); return t.allMethods[i] }
 
 // Empty reports whether t is the empty interface.
-func (t *Interface) Empty() bool { return len(t.allMethods) == 0 }
+// The interface must have been completed.
+func (t *Interface) Empty() bool { t.assertCompleteness(); return len(t.allMethods) == 0 }
 
 // Complete computes the interface's method set. It must be called by users of
 // NewInterfaceType and NewInterface after the interface's embedded types are
diff --git a/src/go/types/typexpr.go b/src/go/types/typexpr.go
index 19bedae590..4948b800d1 100644
--- a/src/go/types/typexpr.go
+++ b/src/go/types/typexpr.go
@@ -538,10 +538,10 @@ func (check *Checker) completeInterface(ityp *Interface) {
 		return
 	}
 
-	// completeInterface may be called via the LookupFieldOrMethod or
-	// MissingMethod external API in which case check will be nil. In
-	// this case, type-checking must be finished and all interfaces
-	// should have been completed.
+	// completeInterface may be called via the LookupFieldOrMethod,
+	// MissingMethod, Identical, or IdenticalIgnoreTags external API
+	// in which case check will be nil. In this case, type-checking
+	// must be finished and all interfaces should have been completed.
 	if check == nil {
 		panic("internal error: incomplete interface")
 	}
@@ -569,7 +569,7 @@ func (check *Checker) completeInterface(ityp *Interface) {
 		default:
 			// check method signatures after all types are computed (issue #33656)
 			check.atEnd(func() {
-				if !Identical(m.typ, other.Type()) {
+				if !check.identical(m.typ, other.Type()) {
 					check.errorf(m.pos, "duplicate method %s", m.name)
 					check.reportAltDecl(other)
 				}