diff --git a/.travis.yml b/.travis.yml
index 9d9b7f9..0df64f8 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -5,7 +5,7 @@
   - master
 matrix:
   include:
-    - go: 1.6.x
+    - go: 1.8.x
       script: go test -v -race ./...
   allow_failures:
     - go: master
diff --git a/cmp/cmpopts/sort.go b/cmp/cmpopts/sort.go
index a566d24..d2e97dc 100644
--- a/cmp/cmpopts/sort.go
+++ b/cmp/cmpopts/sort.go
@@ -7,6 +7,7 @@
 import (
 	"fmt"
 	"reflect"
+	"sort"
 
 	"github.com/google/go-cmp/cmp"
 	"github.com/google/go-cmp/cmp/internal/function"
@@ -48,8 +49,8 @@
 	}
 	// Check whether the slices are already sorted to avoid an infinite
 	// recursion cycle applying the same transform to itself.
-	ok1 := sliceIsSorted(x, func(i, j int) bool { return ss.less(vx, i, j) })
-	ok2 := sliceIsSorted(y, func(i, j int) bool { return ss.less(vy, i, j) })
+	ok1 := sort.SliceIsSorted(x, func(i, j int) bool { return ss.less(vx, i, j) })
+	ok2 := sort.SliceIsSorted(y, func(i, j int) bool { return ss.less(vy, i, j) })
 	return !ok1 || !ok2
 }
 func (ss sliceSorter) sort(x interface{}) interface{} {
@@ -58,7 +59,7 @@
 	for i := 0; i < src.Len(); i++ {
 		dst.Index(i).Set(src.Index(i))
 	}
-	sortSliceStable(dst.Interface(), func(i, j int) bool { return ss.less(dst, i, j) })
+	sort.SliceStable(dst.Interface(), func(i, j int) bool { return ss.less(dst, i, j) })
 	ss.checkSort(dst)
 	return dst.Interface()
 }
@@ -118,7 +119,10 @@
 }
 func (ms mapSorter) sort(x interface{}) interface{} {
 	src := reflect.ValueOf(x)
-	outType := mapEntryType(src.Type())
+	outType := reflect.StructOf([]reflect.StructField{
+		{Name: "K", Type: src.Type().Key()},
+		{Name: "V", Type: src.Type().Elem()},
+	})
 	dst := reflect.MakeSlice(reflect.SliceOf(outType), src.Len(), src.Len())
 	for i, k := range src.MapKeys() {
 		v := reflect.New(outType).Elem()
@@ -126,7 +130,7 @@
 		v.Field(1).Set(src.MapIndex(k))
 		dst.Index(i).Set(v)
 	}
-	sortSlice(dst.Interface(), func(i, j int) bool { return ms.less(dst, i, j) })
+	sort.Slice(dst.Interface(), func(i, j int) bool { return ms.less(dst, i, j) })
 	ms.checkSort(dst)
 	return dst.Interface()
 }
@@ -139,8 +143,5 @@
 }
 func (ms mapSorter) less(v reflect.Value, i, j int) bool {
 	vx, vy := v.Index(i).Field(0), v.Index(j).Field(0)
-	if !hasReflectStructOf {
-		vx, vy = vx.Elem(), vy.Elem()
-	}
 	return ms.fnc.Call([]reflect.Value{vx, vy})[0].Bool()
 }
diff --git a/cmp/cmpopts/sort_go17.go b/cmp/cmpopts/sort_go17.go
deleted file mode 100644
index 839b88c..0000000
--- a/cmp/cmpopts/sort_go17.go
+++ /dev/null
@@ -1,46 +0,0 @@
-// Copyright 2017, 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.md file.
-
-// +build !go1.8
-
-package cmpopts
-
-import (
-	"reflect"
-	"sort"
-)
-
-const hasReflectStructOf = false
-
-func mapEntryType(reflect.Type) reflect.Type {
-	return reflect.TypeOf(struct{ K, V interface{} }{})
-}
-
-func sliceIsSorted(slice interface{}, less func(i, j int) bool) bool {
-	return sort.IsSorted(reflectSliceSorter{reflect.ValueOf(slice), less})
-}
-func sortSlice(slice interface{}, less func(i, j int) bool) {
-	sort.Sort(reflectSliceSorter{reflect.ValueOf(slice), less})
-}
-func sortSliceStable(slice interface{}, less func(i, j int) bool) {
-	sort.Stable(reflectSliceSorter{reflect.ValueOf(slice), less})
-}
-
-type reflectSliceSorter struct {
-	slice reflect.Value
-	less  func(i, j int) bool
-}
-
-func (ss reflectSliceSorter) Len() int {
-	return ss.slice.Len()
-}
-func (ss reflectSliceSorter) Less(i, j int) bool {
-	return ss.less(i, j)
-}
-func (ss reflectSliceSorter) Swap(i, j int) {
-	vi := ss.slice.Index(i).Interface()
-	vj := ss.slice.Index(j).Interface()
-	ss.slice.Index(i).Set(reflect.ValueOf(vj))
-	ss.slice.Index(j).Set(reflect.ValueOf(vi))
-}
diff --git a/cmp/cmpopts/sort_go18.go b/cmp/cmpopts/sort_go18.go
deleted file mode 100644
index 8a59c0d..0000000
--- a/cmp/cmpopts/sort_go18.go
+++ /dev/null
@@ -1,31 +0,0 @@
-// Copyright 2017, 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.md file.
-
-// +build go1.8
-
-package cmpopts
-
-import (
-	"reflect"
-	"sort"
-)
-
-const hasReflectStructOf = true
-
-func mapEntryType(t reflect.Type) reflect.Type {
-	return reflect.StructOf([]reflect.StructField{
-		{Name: "K", Type: t.Key()},
-		{Name: "V", Type: t.Elem()},
-	})
-}
-
-func sliceIsSorted(slice interface{}, less func(i, j int) bool) bool {
-	return sort.SliceIsSorted(slice, less)
-}
-func sortSlice(slice interface{}, less func(i, j int) bool) {
-	sort.Slice(slice, less)
-}
-func sortSliceStable(slice interface{}, less func(i, j int) bool) {
-	sort.SliceStable(slice, less)
-}
diff --git a/cmp/cmpopts/util_test.go b/cmp/cmpopts/util_test.go
index f532789..1140941 100644
--- a/cmp/cmpopts/util_test.go
+++ b/cmp/cmpopts/util_test.go
@@ -719,7 +719,7 @@
 	}}
 
 	for _, tt := range tests {
-		tRun(t, tt.label, func(t *testing.T) {
+		t.Run(tt.label, func(t *testing.T) {
 			var gotEqual bool
 			var gotPanic string
 			func() {
@@ -939,7 +939,7 @@
 	}}
 
 	for _, tt := range tests {
-		tRun(t, tt.label, func(t *testing.T) {
+		t.Run(tt.label, func(t *testing.T) {
 			// Prepare function arguments.
 			vf := reflect.ValueOf(tt.fnc)
 			var vargs []reflect.Value
@@ -980,17 +980,3 @@
 		})
 	}
 }
-
-// TODO: Delete this hack when we drop Go1.6 support.
-func tRun(t *testing.T, name string, f func(t *testing.T)) {
-	type runner interface {
-		Run(string, func(t *testing.T)) bool
-	}
-	var ti interface{} = t
-	if r, ok := ti.(runner); ok {
-		r.Run(name, f)
-	} else {
-		t.Logf("Test: %s", name)
-		f(t)
-	}
-}
diff --git a/cmp/compare_test.go b/cmp/compare_test.go
index 6a69ad3..f596788 100644
--- a/cmp/compare_test.go
+++ b/cmp/compare_test.go
@@ -51,7 +51,8 @@
 
 	for _, tt := range tests {
 		tt := tt
-		tRunParallel(t, tt.label, func(t *testing.T) {
+		t.Run(tt.label, func(t *testing.T) {
+			t.Parallel()
 			var gotDiff, gotPanic string
 			func() {
 				defer func() {
@@ -1928,21 +1929,3 @@
 	+: <non-existent>`,
 	}}
 }
-
-// TODO: Delete this hack when we drop Go1.6 support.
-func tRunParallel(t *testing.T, name string, f func(t *testing.T)) {
-	type runner interface {
-		Run(string, func(t *testing.T)) bool
-	}
-	var ti interface{} = t
-	if r, ok := ti.(runner); ok {
-		r.Run(name, func(t *testing.T) {
-			t.Parallel()
-			f(t)
-		})
-	} else {
-		// Cannot run sub-tests in parallel in Go1.6.
-		t.Logf("Test: %s", name)
-		f(t)
-	}
-}
diff --git a/cmp/internal/diff/diff_test.go b/cmp/internal/diff/diff_test.go
index 6399509..0752f4a 100644
--- a/cmp/internal/diff/diff_test.go
+++ b/cmp/internal/diff/diff_test.go
@@ -242,7 +242,7 @@
 	}}
 
 	for _, tt := range tests {
-		tRun(t, "", func(t *testing.T) {
+		t.Run("", func(t *testing.T) {
 			x := strings.Replace(tt.x, " ", "", -1)
 			y := strings.Replace(tt.y, " ", "", -1)
 			es := testStrings(t, x, y)
@@ -273,10 +273,10 @@
 	}
 
 	for i, tt := range tests {
-		tRun(t, fmt.Sprintf("P%d", i), func(t *testing.T) {
+		t.Run(fmt.Sprintf("P%d", i), func(t *testing.T) {
 			// Sweep from 1B to 1KiB.
 			for n := 1; n <= 1024; n <<= 1 {
-				tRun(t, fmt.Sprintf("N%d", n), func(t *testing.T) {
+				t.Run(fmt.Sprintf("N%d", n), func(t *testing.T) {
 					for j := 0; j < 10; j++ {
 						x, y := generateStrings(n, tt.px, tt.py, tt.pm, int64(j))
 						testStrings(t, x, y)
@@ -287,23 +287,20 @@
 	}
 }
 
-func benchmarkDifference(b *testing.B, n int) {
-	// TODO: Use testing.B.Run when we drop Go1.6 support.
-	x, y := generateStrings(n, 0.05, 0.05, 0.10, 0)
-	b.ReportAllocs()
-	b.SetBytes(int64(len(x) + len(y)))
-	for i := 0; i < b.N; i++ {
-		Difference(len(x), len(y), func(ix, iy int) Result {
-			return compareByte(x[ix], y[iy])
+func BenchmarkDifference(b *testing.B) {
+	for n := 1 << 10; n <= 1<<20; n <<= 2 {
+		b.Run(fmt.Sprintf("N%d", n), func(b *testing.B) {
+			x, y := generateStrings(n, 0.05, 0.05, 0.10, 0)
+			b.ReportAllocs()
+			b.SetBytes(int64(len(x) + len(y)))
+			for i := 0; i < b.N; i++ {
+				Difference(len(x), len(y), func(ix, iy int) Result {
+					return compareByte(x[ix], y[iy])
+				})
+			}
 		})
 	}
 }
-func BenchmarkDifference1K(b *testing.B)   { benchmarkDifference(b, 1<<10) }
-func BenchmarkDifference4K(b *testing.B)   { benchmarkDifference(b, 1<<12) }
-func BenchmarkDifference16K(b *testing.B)  { benchmarkDifference(b, 1<<14) }
-func BenchmarkDifference64K(b *testing.B)  { benchmarkDifference(b, 1<<16) }
-func BenchmarkDifference256K(b *testing.B) { benchmarkDifference(b, 1<<18) }
-func BenchmarkDifference1M(b *testing.B)   { benchmarkDifference(b, 1<<20) }
 
 func generateStrings(n int, px, py, pm float32, seed int64) (string, string) {
 	if px+py+pm > 1.0 {
@@ -445,17 +442,3 @@
 		}
 	}
 }
-
-// TODO: Delete this hack when we drop Go1.6 support.
-func tRun(t *testing.T, name string, f func(t *testing.T)) {
-	type runner interface {
-		Run(string, func(t *testing.T)) bool
-	}
-	var ti interface{} = t
-	if r, ok := ti.(runner); ok {
-		r.Run(name, f)
-	} else {
-		t.Logf("Test: %s", name)
-		f(t)
-	}
-}
diff --git a/cmp/internal/value/sort.go b/cmp/internal/value/sort.go
index fe8aa27..938f646 100644
--- a/cmp/internal/value/sort.go
+++ b/cmp/internal/value/sort.go
@@ -19,7 +19,7 @@
 	}
 
 	// Sort the map keys.
-	sort.Sort(valueSorter(vs))
+	sort.Slice(vs, func(i, j int) bool { return isLess(vs[i], vs[j]) })
 
 	// Deduplicate keys (fails for NaNs).
 	vs2 := vs[:1]
@@ -31,13 +31,6 @@
 	return vs2
 }
 
-// TODO: Use sort.Slice once Google AppEngine is on Go1.8 or above.
-type valueSorter []reflect.Value
-
-func (vs valueSorter) Len() int           { return len(vs) }
-func (vs valueSorter) Less(i, j int) bool { return isLess(vs[i], vs[j]) }
-func (vs valueSorter) Swap(i, j int)      { vs[i], vs[j] = vs[j], vs[i] }
-
 // isLess is a generic function for sorting arbitrary map keys.
 // The inputs must be of the same type and must be comparable.
 func isLess(x, y reflect.Value) bool {
diff --git a/cmp/options_test.go b/cmp/options_test.go
index 009b524..7d1af1c 100644
--- a/cmp/options_test.go
+++ b/cmp/options_test.go
@@ -185,7 +185,7 @@
 	}}
 
 	for _, tt := range tests {
-		tRun(t, tt.label, func(t *testing.T) {
+		t.Run(tt.label, func(t *testing.T) {
 			var gotPanic string
 			func() {
 				defer func() {
@@ -215,17 +215,3 @@
 		})
 	}
 }
-
-// TODO: Delete this hack when we drop Go1.6 support.
-func tRun(t *testing.T, name string, f func(t *testing.T)) {
-	type runner interface {
-		Run(string, func(t *testing.T)) bool
-	}
-	var ti interface{} = t
-	if r, ok := ti.(runner); ok {
-		r.Run(name, f)
-	} else {
-		t.Logf("Test: %s", name)
-		f(t)
-	}
-}