diff --git a/README.md b/README.md
index 6ff1458..6657e03 100644
--- a/README.md
+++ b/README.md
@@ -2,8 +2,7 @@
 
 	GO111MODULE=on go get mvdan.cc/garble
 
-Obfuscate Go code by wrapping the Go toolchain. Requires Go 1.15.x; note that
-support for Go 1.16 is [a work in progress](https://github.com/burrowers/garble/issues/124).
+Obfuscate Go code by wrapping the Go toolchain. Requires Go 1.15 or later.
 
 	garble build [build flags] [packages]
 
diff --git a/main.go b/main.go
index a31d3f3..1842b51 100644
--- a/main.go
+++ b/main.go
@@ -186,8 +186,8 @@ var errJustExit = errors.New("")
 
 func goVersionOK() bool {
 	const (
-		minGoVersion        = "v1.15.0"
-		supportedGoVersions = "1.15.x"
+		minGoVersion       = "v1.15.0"
+		suggestedGoVersion = "1.16.x"
 
 		gitTimeFormat = "Mon Jan 2 15:04:05 2006 -0700"
 	)
@@ -195,7 +195,8 @@ func goVersionOK() bool {
 	minGoVersionDate := time.Date(2020, 8, 11, 0, 0, 0, 0, time.UTC)
 
 	out, err := exec.Command("go", "version").CombinedOutput()
-	if err != nil {
+	rawVersion := strings.TrimSpace(string(out))
+	if err != nil || !strings.HasPrefix(rawVersion, "go version ") {
 		fmt.Fprintf(os.Stderr, `Can't get Go version: %v
 
 This is likely due to go not being installed/setup correctly.
@@ -205,7 +206,7 @@ How to install Go: https://golang.org/doc/install
 		return false
 	}
 
-	rawVersion := strings.TrimPrefix(strings.TrimSpace(string(out)), "go version ")
+	rawVersion = strings.TrimPrefix(rawVersion, "go version ")
 
 	tagIdx := strings.IndexByte(rawVersion, ' ')
 	tag := rawVersion[:tagIdx]
@@ -230,13 +231,13 @@ How to install Go: https://golang.org/doc/install
 			return true
 		}
 
-		fmt.Fprintf(os.Stderr, "You use the old unstable %q Go version, please upgrade Go to %s\n", rawVersion, supportedGoVersions)
+		fmt.Fprintf(os.Stderr, "Go version %q is too old; please upgrade to Go %s or a newer devel version\n", rawVersion, suggestedGoVersion)
 		return false
 	}
 
 	version := "v" + strings.TrimPrefix(tag, "go")
 	if semver.Compare(version, minGoVersion) < 0 {
-		fmt.Fprintf(os.Stderr, "Outdated Go version %q is used, please upgrade Go to %s\n", version, supportedGoVersions)
+		fmt.Fprintf(os.Stderr, "Go version %q is too old; please upgrade to Go %s\n", rawVersion, suggestedGoVersion)
 		return false
 	}
 
diff --git a/testdata/scripts/goversion.txt b/testdata/scripts/goversion.txt
index d33c0fb..7873b34 100644
--- a/testdata/scripts/goversion.txt
+++ b/testdata/scripts/goversion.txt
@@ -1,51 +1,68 @@
-chmod 777 .bin/go
+# We use a simple Go program to report many Go versions.
+# The program also errors on any command other than "go version",
+# which saves us having to rebuild main.go many times.
+go build -o .bin/go$exe ./fakego
 env PATH=${WORK}/.bin${:}${PATH}
 
-# Check incorrect go install
+# An empty go version.
 env GO_VERSION=''
 ! garble build
 stderr 'Can''t get Go version'
 
-[short] stop
-
-# Check invalid devel format
+# An invalid devel string.
 env GO_VERSION='go version devel someinvalidversion'
 ! garble build
 stderr 'Can''t recognize devel build timestamp'
 
-# Check invalid devel date
+# An invalid devel date.
 env GO_VERSION='go version devel +afb5fca Sun Sep 99 99:99:99 9999 +0000 linux/amd64'
 ! garble build
 stderr 'Can''t recognize devel build timestamp: parsing time'
 
-# Check invalid old devel version
+# 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 'You use the old unstable'
+stderr 'Go version.*Aug 07.*too old; please upgrade to Go 1.16.x or a newer devel version'
 
-# Check invalid new 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'
 ! garble build
-! stderr 'You use the old unstable'
+stderr 'mocking the real build'
 
-# Check old version
+# We should error on a stable version that's too old.
 env GO_VERSION='go version go1.14 windows/amd64'
 ! garble build
-stderr 'Outdated Go version'
+stderr 'Go version.*go1.14.*too old; please upgrade to Go 1.16.x'
+! stderr 'or a newer devel version'
 
-# Check supported version
+# We should accept a supported stable version.
 env GO_VERSION='go version go1.15.2 windows/amd64'
 ! garble build
-! stderr 'Outdated Go version'
+stderr 'mocking the real build'
+
+-- go.mod --
+module test/main
 
+go 1.15
 -- main.go --
 package main
 
--- .bin/go --
-#!/bin/sh
+func main() {}
+
+-- fakego/main.go --
+package main
 
-[ -z "$GO_VERSION" ] && exit 1 || echo "$GO_VERSION"
+import (
+	"fmt"
+	"os"
+)
 
--- .bin/go.bat --
-@echo off
-IF DEFINED GO_VERSION (echo %GO_VERSION%) ELSE (exit 1)
+func main() {
+	if len(os.Args) > 0 && os.Args[1] == "version" {
+		fmt.Println(os.Getenv("GO_VERSION"))
+		return
+	}
+	fmt.Fprintln(os.Stderr, "mocking the real build")
+	os.Exit(1)
+}