diff --git a/.github/workflows/test.yml b/.github/workflows/test.yml
index 67fe24c..8bec42b 100644
--- a/.github/workflows/test.yml
+++ b/.github/workflows/test.yml
@@ -10,7 +10,7 @@ jobs:
   test:
     strategy:
       matrix:
-        go-version: [1.15.x, 1.16.x]
+        go-version: [1.16.x]
         platform: [ubuntu-latest, macos-latest, windows-latest]
     runs-on: ${{ matrix.platform }}
     steps:
diff --git a/README.md b/README.md
index d111c46..e74a3de 100644
--- a/README.md
+++ b/README.md
@@ -2,7 +2,7 @@
 
 	GO111MODULE=on go get mvdan.cc/garble
 
-Obfuscate Go code by wrapping the Go toolchain. Requires Go 1.15 or later.
+Obfuscate Go code by wrapping the Go toolchain. Requires Go 1.16 or later.
 
 	garble build [build flags] [packages]
 
@@ -41,12 +41,12 @@ what packages to obfuscate, set `GOPRIVATE`, documented at `go help private`.
 Note that commands like `garble build` will use the `go` version found in your
 `$PATH`. To use different versions of Go, you can
 [install them](https://golang.org/doc/manage-install#installing-multiple)
-and set up `$PATH` with them. For example, for Go 1.15.8:
+and set up `$PATH` with them. For example, for Go 1.16.1:
 
 ```sh
-$ go get golang.org/dl/go1.15.8
-$ go1.15.8 download
-$ PATH=$(go1.15.8 env GOROOT)/bin:${PATH} garble build
+$ go get golang.org/dl/go1.16.1
+$ go1.16.1 download
+$ PATH=$(go1.16.1 env GOROOT)/bin:${PATH} garble build
 ```
 
 You can also declare a function to make multiple uses simpler:
@@ -58,7 +58,7 @@ $ withgo() {
 
 	PATH=$(${gocmd} env GOROOT)/bin:${PATH} "$@"
 }
-$ withgo 1.15.8 garble build
+$ withgo 1.16.1 garble build
 ```
 
 ### Caveats
diff --git a/go.mod b/go.mod
index 6d5816c..b644b6c 100644
--- a/go.mod
+++ b/go.mod
@@ -1,10 +1,10 @@
 module mvdan.cc/garble
 
-go 1.15
+go 1.16
 
 require (
-	github.com/google/go-cmp v0.5.4
+	github.com/google/go-cmp v0.5.5
 	github.com/rogpeppe/go-internal v1.7.1-0.20210131190821-dc4b49510d96
 	golang.org/x/mod v0.4.1
-	golang.org/x/tools v0.0.0-20210115202250-e0d201561e39
+	golang.org/x/tools v0.1.1-0.20210304221016-50ca8d007de9
 )
diff --git a/go.sum b/go.sum
index 6f9f6b0..fa5b8db 100644
--- a/go.sum
+++ b/go.sum
@@ -1,5 +1,5 @@
-github.com/google/go-cmp v0.5.4 h1:L8R9j+yAqZuZjsqh/z+F1NCffTKKLShY6zXTItVIZ8M=
-github.com/google/go-cmp v0.5.4/go.mod h1:v8dTdLbMG2kIc/vJvl+f65V22dbkXbowE6jgT/gNBxE=
+github.com/google/go-cmp v0.5.5 h1:Khx7svrCpmxxtHBq5j2mp/xVjsi8hQMfNLvJFAlrGgU=
+github.com/google/go-cmp v0.5.5/go.mod h1:v8dTdLbMG2kIc/vJvl+f65V22dbkXbowE6jgT/gNBxE=
 github.com/kr/pretty v0.1.0 h1:L/CwN0zerZDmRFUapSPitk6f+Q3+0za1rQkzVuMiMFI=
 github.com/kr/pretty v0.1.0/go.mod h1:dAy3ld7l9f0ibDNOQOHHMYYIIbhfbHSm3C4ZsoJORNo=
 github.com/kr/pty v1.1.1/go.mod h1:pFQYn66WHrOpPYNljwOMqo10TkYh1fy3cYio2l3bCsQ=
@@ -11,7 +11,6 @@ github.com/yuin/goldmark v1.2.1/go.mod h1:3hX8gzYuyVAZsxl0MRgGTJEmQBFcNTphYh9dec
 golang.org/x/crypto v0.0.0-20190308221718-c2843e01d9a2/go.mod h1:djNgcEr1/C05ACkg1iLfiJU5Ep61QUkGW8qpdssI0+w=
 golang.org/x/crypto v0.0.0-20191011191535-87dc89f01550/go.mod h1:yigFU9vqHzYiE8UmvKecakEJjdnWj3jj499lnFckfCI=
 golang.org/x/crypto v0.0.0-20200622213623-75b288015ac9/go.mod h1:LzIPMQfyMNhhGPhUkYOs5KpL4U8rLKemX1yGLhDgUto=
-golang.org/x/mod v0.3.0/go.mod h1:s0Qsj1ACt9ePp/hMypM3fl4fZqREWJwdYDEqhRiZZUA=
 golang.org/x/mod v0.4.1 h1:Kvvh58BN8Y9/lBi7hTekvtMpm07eUZ0ck5pRHpsMWrY=
 golang.org/x/mod v0.4.1/go.mod h1:s0Qsj1ACt9ePp/hMypM3fl4fZqREWJwdYDEqhRiZZUA=
 golang.org/x/net v0.0.0-20190404232315-eb5bcb51f2a3/go.mod h1:t9HGtf8HONx5eT2rtn7q6eTqICYqUVnKs3thJo3Qplg=
@@ -22,12 +21,13 @@ golang.org/x/sync v0.0.0-20201020160332-67f06af15bc9/go.mod h1:RxMgew5VJxzue5/jJ
 golang.org/x/sys v0.0.0-20190215142949-d0b11bdaac8a/go.mod h1:STP8DvDyc/dI5b8T5hshtkjS+E42TnysNCUPdjciGhY=
 golang.org/x/sys v0.0.0-20190412213103-97732733099d/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
 golang.org/x/sys v0.0.0-20200930185726-fdedc70b468f/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
+golang.org/x/sys v0.0.0-20210124154548-22da62e12c0c/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
 golang.org/x/text v0.3.0/go.mod h1:NqM8EUOU14njkJ3fqMW+pc6Ldnwhi/IjpwHt7yyuwOQ=
 golang.org/x/text v0.3.3/go.mod h1:5Zoc/QRtKVWzQhOtBMvqHzDpF6irO9z98xDceosuGiQ=
 golang.org/x/tools v0.0.0-20180917221912-90fa682c2a6e/go.mod h1:n7NCudcB/nEzxVGmLbDWY5pfWTLqBcC2KZ6jyYvM4mQ=
 golang.org/x/tools v0.0.0-20191119224855-298f0cb1881e/go.mod h1:b+2E5dAYhXwXZwtnZ6UAqBI28+e2cm9otk0dWdXHAEo=
-golang.org/x/tools v0.0.0-20210115202250-e0d201561e39 h1:BTs2GMGSMWpgtCpv1CE7vkJTv7XcHdcLLnAMu7UbgTY=
-golang.org/x/tools v0.0.0-20210115202250-e0d201561e39/go.mod h1:emZCQorbCU4vsT4fOWvOPXz4eW1wZW4PmDk9uLelYpA=
+golang.org/x/tools v0.1.1-0.20210304221016-50ca8d007de9 h1:lQ9QDTM4SHDP/S/bmj2wjNMQ93AvRYf7kuoqr2MDxmc=
+golang.org/x/tools v0.1.1-0.20210304221016-50ca8d007de9/go.mod h1:9bzcO0MWcOuT0tm1iBGzDVPshzfwoVvREIui8C+MHqU=
 golang.org/x/xerrors v0.0.0-20190717185122-a985d3407aa7/go.mod h1:I/5z698sn9Ka8TeJc9MKroUUfqBBauWjQqLJ2OPfmY0=
 golang.org/x/xerrors v0.0.0-20191011141410-1b5146add898/go.mod h1:I/5z698sn9Ka8TeJc9MKroUUfqBBauWjQqLJ2OPfmY0=
 golang.org/x/xerrors v0.0.0-20191204190536-9bdfabe68543/go.mod h1:I/5z698sn9Ka8TeJc9MKroUUfqBBauWjQqLJ2OPfmY0=
diff --git a/main.go b/main.go
index 34b204f..7f4be49 100644
--- a/main.go
+++ b/main.go
@@ -166,13 +166,13 @@ var errJustExit = errors.New("")
 
 func goVersionOK() bool {
 	const (
-		minGoVersion       = "v1.15.0"
+		minGoVersion       = "v1.16.0"
 		suggestedGoVersion = "1.16.x"
 
 		gitTimeFormat = "Mon Jan 2 15:04:05 2006 -0700"
 	)
-	// Go 1.15 was released on August 11th, 2020.
-	minGoVersionDate := time.Date(2020, 8, 11, 0, 0, 0, 0, time.UTC)
+	// Go 1.16 was released on Febuary 16th, 2021.
+	minGoVersionDate := time.Date(2021, 2, 16, 0, 0, 0, 0, time.UTC)
 
 	out, err := exec.Command("go", "version").CombinedOutput()
 	rawVersion := strings.TrimSpace(string(out))
@@ -811,21 +811,13 @@ var runtimeRelated = map[string]bool{
 	"vendor/golang.org/x/net/dns/dnsmessage": true,
 	"vendor/golang.org/x/net/route":          true,
 
-	// These packages were moved in Go 1.16, but 1.15's runtime still
-	// linknames to them.
-	"io/ioutil":     true,
-	"path/filepath": true,
-
-	// Go 1.15's "net" package depends on "math/rand", but 1.16's does not.
-	// Keep it here to support 1.15.
-	"math/rand": true,
-
 	// These packages call pure Go functions from assembly functions.
 	// We obfuscate the pure Go function name, breaking the assembly.
 	// We do not deal with that edge case just yet, so for now,
 	// never obfuscate these packages.
 	// TODO: remove once we fix issue 261.
 	"math/big":      true,
+	"math/rand":     true,
 	"crypto/sha512": true,
 	"crypto":        true,
 }
diff --git a/main_test.go b/main_test.go
index e40d23d..1d5b685 100644
--- a/main_test.go
+++ b/main_test.go
@@ -60,7 +60,6 @@ func TestScripts(t *testing.T) {
 			env.Vars = append(env.Vars,
 				"GOPROXY="+proxyURL,
 				"GONOSUMDB=*",
-				"GOFLAGS=-mod=readonly", // TODO(mvdan): remove once we switch to Go 1.16
 				"gofullversion="+runtime.Version(),
 			)
 
diff --git a/runtime_strip.go b/runtime_strip.go
index ac78644..1448070 100644
--- a/runtime_strip.go
+++ b/runtime_strip.go
@@ -123,7 +123,6 @@ func stripRuntime(filename string, file *ast.File) {
 	case "runtime1.go":
 		// On Go 1.16.x, the code above results in runtime1.go having an
 		// unused import. Mark it as used via "var _ = pkg.Func".
-		// Note that the file in Go 1.15.x does not import bytealg.
 		// If this is a recurring problem, we could go for a more
 		// generic solution like x/tools/imports.
 		for _, imp := range file.Imports {
diff --git a/shared.go b/shared.go
index 0877b3f..369e955 100644
--- a/shared.go
+++ b/shared.go
@@ -218,15 +218,7 @@ func setListedPackages(patterns []string) error {
 			return err
 		}
 		if pkg.Export != "" {
-			buildID := pkg.BuildID
-			if buildID == "" {
-				// go list only includes BuildID in 1.16+
-				buildID, err = buildidOf(pkg.Export)
-				if err != nil {
-					panic(err) // shouldn't happen
-				}
-			}
-			actionID := decodeHash(splitActionID(buildID))
+			actionID := decodeHash(splitActionID(pkg.BuildID))
 			h := sha256.New()
 			h.Write(actionID)
 			h.Write(cache.BinaryContentID)
diff --git a/testdata/scripts/asm.txt b/testdata/scripts/asm.txt
index 47b5b9e..522d861 100644
--- a/testdata/scripts/asm.txt
+++ b/testdata/scripts/asm.txt
@@ -19,7 +19,7 @@ cmp stderr main.stderr
 -- go.mod --
 module test/main
 
-go 1.15
+go 1.16
 -- main.go --
 package main
 
diff --git a/testdata/scripts/basic.txt b/testdata/scripts/basic.txt
index ee2dbc2..604805d 100644
--- a/testdata/scripts/basic.txt
+++ b/testdata/scripts/basic.txt
@@ -58,7 +58,7 @@ binsubstr main$exe 'main.go' 'globalVar' 'globalFunc' $gofullversion
 -- go.mod --
 module test/mainfoo
 
-go 1.15
+go 1.16
 -- main.go --
 package main
 
diff --git a/testdata/scripts/cgo.txt b/testdata/scripts/cgo.txt
index 99369e2..409253c 100644
--- a/testdata/scripts/cgo.txt
+++ b/testdata/scripts/cgo.txt
@@ -19,7 +19,7 @@ cmp stderr main.stderr
 -- go.mod --
 module test/main
 
-go 1.15
+go 1.16
 -- main.go --
 package main
 
diff --git a/testdata/scripts/debugdir.txt b/testdata/scripts/debugdir.txt
index ef575a2..8243200 100644
--- a/testdata/scripts/debugdir.txt
+++ b/testdata/scripts/debugdir.txt
@@ -18,7 +18,7 @@ stderr 'test/main' # we force rebuilds with -debugdir
 -- go.mod --
 module test/main
 
-go 1.15
+go 1.16
 -- main.go --
 package main
 
diff --git a/testdata/scripts/goprivate.txt b/testdata/scripts/goprivate.txt
index 9a6c0b4..39c42bf 100644
--- a/testdata/scripts/goprivate.txt
+++ b/testdata/scripts/goprivate.txt
@@ -26,7 +26,7 @@ garble build -o=out ./stdimporter
 -- go.mod --
 module test/main
 
-go 1.15
+go 1.16
 -- standalone/main.go --
 package main
 
diff --git a/testdata/scripts/goversion.txt b/testdata/scripts/goversion.txt
index 7873b34..58eba11 100644
--- a/testdata/scripts/goversion.txt
+++ b/testdata/scripts/goversion.txt
@@ -20,13 +20,12 @@ env GO_VERSION='go version devel +afb5fca Sun Sep 99 99:99:99 9999 +0000 linux/a
 stderr 'Can''t recognize devel build timestamp: parsing time'
 
 # We should error on a devel version that's too old.
-# We support Go 1.15 and later, released on August 11th, 2020.
 env GO_VERSION='go version devel +afb5fca Sun Aug 07 00:00:00 2020 +0000 linux/amd64'
 ! garble build
 stderr 'Go version.*Aug 07.*too old; please upgrade to Go 1.16.x or a newer devel version'
 
-# A recent enough devel timestamp should be fine.
-env GO_VERSION='go version devel +afb5fca Sun Sep 13 07:54:42 2020 +0000 linux/amd64'
+# A future devel timestamp should be fine.
+env GO_VERSION='go version devel +afb5fca Sun Sep 13 07:54:42 2021 +0000 linux/amd64'
 ! garble build
 stderr 'mocking the real build'
 
@@ -36,15 +35,15 @@ env GO_VERSION='go version go1.14 windows/amd64'
 stderr 'Go version.*go1.14.*too old; please upgrade to Go 1.16.x'
 ! stderr 'or a newer devel version'
 
-# We should accept a supported stable version.
-env GO_VERSION='go version go1.15.2 windows/amd64'
+# We should accept a future stable version.
+env GO_VERSION='go version go1.16.2 windows/amd64'
 ! garble build
 stderr 'mocking the real build'
 
 -- go.mod --
 module test/main
 
-go 1.15
+go 1.16
 -- main.go --
 package main
 
diff --git a/testdata/scripts/implement.txt b/testdata/scripts/implement.txt
index 44a7a6d..06ce3f8 100644
--- a/testdata/scripts/implement.txt
+++ b/testdata/scripts/implement.txt
@@ -9,7 +9,7 @@ cmp stderr main.stderr
 -- go.mod --
 module test/main
 
-go 1.15
+go 1.16
 -- main.go --
 package main
 
diff --git a/testdata/scripts/imports.txt b/testdata/scripts/imports.txt
index f47f279..41b3248 100644
--- a/testdata/scripts/imports.txt
+++ b/testdata/scripts/imports.txt
@@ -45,7 +45,7 @@ cmp stdout main.stdout
 -- go.mod --
 module test/main
 
-go 1.15
+go 1.16
 
 require (
 	rsc.io/quote v1.5.2
diff --git a/testdata/scripts/init.txt b/testdata/scripts/init.txt
index a9ccc51..f3364d2 100644
--- a/testdata/scripts/init.txt
+++ b/testdata/scripts/init.txt
@@ -13,7 +13,7 @@ cmp stderr main.stderr
 -- go.mod --
 module test/main
 
-go 1.15
+go 1.16
 -- main.go --
 package main
 
diff --git a/testdata/scripts/ldflags.txt b/testdata/scripts/ldflags.txt
index 3a7acc0..c76fe31 100644
--- a/testdata/scripts/ldflags.txt
+++ b/testdata/scripts/ldflags.txt
@@ -23,7 +23,7 @@ binsubstr main$exe 'unexportedVersion'
 -- go.mod --
 module domain.test/main
 
-go 1.15
+go 1.16
 -- main.go --
 package main
 
diff --git a/testdata/scripts/linkname.txt b/testdata/scripts/linkname.txt
index 7333af6..ef78e57 100644
--- a/testdata/scripts/linkname.txt
+++ b/testdata/scripts/linkname.txt
@@ -15,7 +15,7 @@ cmp stderr main.stderr
 -- go.mod --
 module test/main
 
-go 1.15
+go 1.16
 -- main.go --
 package main
 
diff --git a/testdata/scripts/literals.txt b/testdata/scripts/literals.txt
index fb88970..8514ee5 100644
--- a/testdata/scripts/literals.txt
+++ b/testdata/scripts/literals.txt
@@ -55,7 +55,7 @@ grep '^\s+type \w+ func\(byte\) \w+$' .obf-src/main/extra_literals.go
 -- go.mod --
 module test/main
 
-go 1.15
+go 1.16
 -- main.go --
 package main
 
diff --git a/testdata/scripts/modinfo.txt b/testdata/scripts/modinfo.txt
index 614f2dc..970ba40 100644
--- a/testdata/scripts/modinfo.txt
+++ b/testdata/scripts/modinfo.txt
@@ -15,7 +15,7 @@ binsubstr main$exe '(devel)'
 -- go.mod --
 module test/main
 
-go 1.15
+go 1.16
 -- main.go --
 package main
 
diff --git a/testdata/scripts/plugin.txt b/testdata/scripts/plugin.txt
index 11a677d..762eabb 100644
--- a/testdata/scripts/plugin.txt
+++ b/testdata/scripts/plugin.txt
@@ -29,7 +29,7 @@ cmp stderr main.stderr
 -- go.mod --
 module test/main
 
-go 1.15
+go 1.16
 -- plugin/main.go --
 package main
 
diff --git a/testdata/scripts/position.txt b/testdata/scripts/position.txt
index f8fa909..186c26e 100644
--- a/testdata/scripts/position.txt
+++ b/testdata/scripts/position.txt
@@ -17,7 +17,7 @@ stdout 'varLines is sorted'
 -- go.mod --
 module test/main
 
-go 1.15
+go 1.16
 -- main.go --
 package main
 
diff --git a/testdata/scripts/reverse.txt b/testdata/scripts/reverse.txt
index 0721d1c..a04c5be 100644
--- a/testdata/scripts/reverse.txt
+++ b/testdata/scripts/reverse.txt
@@ -30,7 +30,7 @@ cmp stderr reverse.stdout
 -- go.mod --
 module test/main
 
-go 1.15
+go 1.16
 -- main.go --
 package main
 
diff --git a/testdata/scripts/seed.txt b/testdata/scripts/seed.txt
index 4dfd755..01bbe08 100644
--- a/testdata/scripts/seed.txt
+++ b/testdata/scripts/seed.txt
@@ -40,7 +40,7 @@ stderr .
 -- go.mod --
 module test/main
 
-go 1.15
+go 1.16
 -- main.go --
 package main
 
diff --git a/testdata/scripts/syntax.txt b/testdata/scripts/syntax.txt
index b964fed..2befd78 100644
--- a/testdata/scripts/syntax.txt
+++ b/testdata/scripts/syntax.txt
@@ -13,13 +13,13 @@ go build
 exec ./main$exe
 cmp stderr main.stderr
 
-binsubstr main$exe 'globalVar' # 'globalType' only matches on go < 1.15
+binsubstr main$exe 'globalVar' # 'globalType' matches on some, but not all, platforms
 ! binsubstr main$exe 'localName' 'globalConst' 'remoteIntReturn' 'intReturn'
 
 -- extra/go.mod --
 module private.source/extra
 
-go 1.15
+go 1.16
 -- extra/extra.go --
 package extra
 
@@ -29,7 +29,7 @@ func Func() string {
 -- go.mod --
 module test/main
 
-go 1.15
+go 1.16
 
 // We include an extra module to obfuscate, included in the same original source
 // code via a replace directive.
diff --git a/testdata/scripts/test.txt b/testdata/scripts/test.txt
index 5f9a5ba..7f409fc 100644
--- a/testdata/scripts/test.txt
+++ b/testdata/scripts/test.txt
@@ -22,7 +22,7 @@ stdout 'PASS.*TestFoo'
 -- go.mod --
 module test/bar
 
-go 1.15
+go 1.16
 -- bar.go --
 package bar
 
diff --git a/testdata/scripts/tiny.txt b/testdata/scripts/tiny.txt
index 93194d9..5397371 100644
--- a/testdata/scripts/tiny.txt
+++ b/testdata/scripts/tiny.txt
@@ -27,7 +27,7 @@ stderr 'panic: oh noes'
 -- go.mod --
 module test/main
 
-go 1.15
+go 1.16
 -- main.go --
 package main