diff --git a/src/cmd/compile/internal/types2/lookup.go b/src/cmd/compile/internal/types2/lookup.go
index 5f76752086..3e04798815 100644
--- a/src/cmd/compile/internal/types2/lookup.go
+++ b/src/cmd/compile/internal/types2/lookup.go
@@ -261,10 +261,18 @@ func lookupType(m map[Type]int, typ Type) (int, bool) {
 }
 
 type instanceLookup struct {
-	m map[*Named][]*Named
+	// buf is used to avoid allocating the map m in the common case of a small
+	// number of instances.
+	buf [3]*Named
+	m   map[*Named][]*Named
 }
 
 func (l *instanceLookup) lookup(inst *Named) *Named {
+	for _, t := range l.buf {
+		if t != nil && Identical(inst, t) {
+			return t
+		}
+	}
 	for _, t := range l.m[inst.Origin()] {
 		if Identical(inst, t) {
 			return t
@@ -274,6 +282,12 @@ func (l *instanceLookup) lookup(inst *Named) *Named {
 }
 
 func (l *instanceLookup) add(inst *Named) {
+	for i, t := range l.buf {
+		if t == nil {
+			l.buf[i] = inst
+			return
+		}
+	}
 	if l.m == nil {
 		l.m = make(map[*Named][]*Named)
 	}
diff --git a/src/cmd/compile/internal/types2/lookup_test.go b/src/cmd/compile/internal/types2/lookup_test.go
new file mode 100644
index 0000000000..56fe48c1e2
--- /dev/null
+++ b/src/cmd/compile/internal/types2/lookup_test.go
@@ -0,0 +1,55 @@
+// Copyright 2022 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package types2_test
+
+import (
+	"path/filepath"
+	"runtime"
+	"testing"
+
+	. "cmd/compile/internal/types2"
+)
+
+// BenchmarkLookupFieldOrMethod measures types.LookupFieldOrMethod performance.
+// LookupFieldOrMethod is a performance hotspot for both type-checking and
+// external API calls.
+func BenchmarkLookupFieldOrMethod(b *testing.B) {
+	// Choose an arbitrary, large package.
+	path := filepath.Join(runtime.GOROOT(), "src", "net", "http")
+
+	files, err := pkgFiles(path)
+	if err != nil {
+		b.Fatal(err)
+	}
+
+	conf := Config{
+		Importer: defaultImporter(),
+	}
+
+	pkg, err := conf.Check("http", files, nil)
+	if err != nil {
+		b.Fatal(err)
+	}
+
+	scope := pkg.Scope()
+	names := scope.Names()
+
+	// Look up an arbitrary name for each type referenced in the package scope.
+	lookup := func() {
+		for _, name := range names {
+			typ := scope.Lookup(name).Type()
+			LookupFieldOrMethod(typ, true, pkg, "m")
+		}
+	}
+
+	// Perform a lookup once, to ensure that any lazily-evaluated state is
+	// complete.
+	lookup()
+
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		lookup()
+	}
+}
diff --git a/src/go/types/lookup.go b/src/go/types/lookup.go
index 9e0a06aedb..828c881367 100644
--- a/src/go/types/lookup.go
+++ b/src/go/types/lookup.go
@@ -261,10 +261,18 @@ func lookupType(m map[Type]int, typ Type) (int, bool) {
 }
 
 type instanceLookup struct {
-	m map[*Named][]*Named
+	// buf is used to avoid allocating the map m in the common case of a small
+	// number of instances.
+	buf [3]*Named
+	m   map[*Named][]*Named
 }
 
 func (l *instanceLookup) lookup(inst *Named) *Named {
+	for _, t := range l.buf {
+		if t != nil && Identical(inst, t) {
+			return t
+		}
+	}
 	for _, t := range l.m[inst.Origin()] {
 		if Identical(inst, t) {
 			return t
@@ -274,6 +282,12 @@ func (l *instanceLookup) lookup(inst *Named) *Named {
 }
 
 func (l *instanceLookup) add(inst *Named) {
+	for i, t := range l.buf {
+		if t == nil {
+			l.buf[i] = inst
+			return
+		}
+	}
 	if l.m == nil {
 		l.m = make(map[*Named][]*Named)
 	}
diff --git a/src/go/types/lookup_test.go b/src/go/types/lookup_test.go
new file mode 100644
index 0000000000..cd5e3fb13d
--- /dev/null
+++ b/src/go/types/lookup_test.go
@@ -0,0 +1,58 @@
+// Copyright 2022 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package types_test
+
+import (
+	"go/importer"
+	"go/token"
+	"path/filepath"
+	"runtime"
+	"testing"
+
+	. "go/types"
+)
+
+// BenchmarkLookupFieldOrMethod measures types.LookupFieldOrMethod performance.
+// LookupFieldOrMethod is a performance hotspot for both type-checking and
+// external API calls.
+func BenchmarkLookupFieldOrMethod(b *testing.B) {
+	// Choose an arbitrary, large package.
+	path := filepath.Join(runtime.GOROOT(), "src", "net", "http")
+
+	fset := token.NewFileSet()
+	files, err := pkgFiles(fset, path, 0)
+	if err != nil {
+		b.Fatal(err)
+	}
+
+	conf := Config{
+		Importer: importer.Default(),
+	}
+
+	pkg, err := conf.Check("http", fset, files, nil)
+	if err != nil {
+		b.Fatal(err)
+	}
+
+	scope := pkg.Scope()
+	names := scope.Names()
+
+	// Look up an arbitrary name for each type referenced in the package scope.
+	lookup := func() {
+		for _, name := range names {
+			typ := scope.Lookup(name).Type()
+			LookupFieldOrMethod(typ, true, pkg, "m")
+		}
+	}
+
+	// Perform a lookup once, to ensure that any lazily-evaluated state is
+	// complete.
+	lookup()
+
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		lookup()
+	}
+}