diff --git a/.travis.yml b/.travis.yml
index 680a500..3073a03 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -39,15 +39,16 @@ env:
   - GO111MODULE=on
   - GOPROXY=https://proxy.golang.org
 
-# When updating Go versions:
-# In addition to changing the "go:" versions below, edit the version
-# test in internal/runtests.sh.
-
 jobs:
+  # When updating Go versions:
+  # In addition to changing the "go:" versions below, edit the version
+  # test in ./internal/runtests.sh.
   include:
-    - go: "1.13.x"
+    - go: "1.15.x"
       os: linux
-    - go: "1.13.x"
+    - go: "1.16.x"
+      os: linux
+    - go: "1.16.x"
       os: osx
-    - go: "1.13.x"
+    - go: "1.16.x"
       os: windows
diff --git a/go.mod b/go.mod
index b2233dc..7335ae1 100644
--- a/go.mod
+++ b/go.mod
@@ -4,7 +4,9 @@ go 1.12
 
 require (
 	github.com/google/go-cmp v0.2.0
-	github.com/google/subcommands v1.0.1
+	github.com/google/subcommands v1.2.0
 	github.com/pmezard/go-difflib v1.0.0
-	golang.org/x/tools v0.0.0-20190422233926-fe54fb35175b
+	golang.org/x/mod v0.4.1 // indirect
+	golang.org/x/sys v0.0.0-20210216224549-f992740a1bac // indirect
+	golang.org/x/tools v0.1.0
 )
diff --git a/go.sum b/go.sum
index 132636d..ff9cc31 100644
--- a/go.sum
+++ b/go.sum
@@ -1,15 +1,34 @@
 github.com/google/go-cmp v0.2.0 h1:+dTQ8DZQJz0Mb/HjFlkptS1FeQ4cWSnN941F8aEG4SQ=
 github.com/google/go-cmp v0.2.0/go.mod h1:oXzfMopK8JAjlY9xF4vHSVASa0yLyX7SntLO5aqRK0M=
-github.com/google/subcommands v1.0.1 h1:/eqq+otEXm5vhfBrbREPCSVQbvofip6kIz+mX5TUH7k=
-github.com/google/subcommands v1.0.1/go.mod h1:ZjhPrFU+Olkh9WazFPsl27BQ4UPiG37m3yTrtFlrHVk=
+github.com/google/subcommands v1.2.0 h1:vWQspBTo2nEqTUFita5/KeEWlUL8kQObDFbub/EN9oE=
+github.com/google/subcommands v1.2.0/go.mod h1:ZjhPrFU+Olkh9WazFPsl27BQ4UPiG37m3yTrtFlrHVk=
 github.com/pmezard/go-difflib v1.0.0 h1:4DBwDE0NGyQoBHbLQYPwSUPoCMWR5BEzIk/f1lZbAQM=
 github.com/pmezard/go-difflib v1.0.0/go.mod h1:iKH77koFhYxTK1pcRnkKkqfTogsbg7gZNVY4sRDYZ/4=
+github.com/yuin/goldmark v1.2.1/go.mod h1:3hX8gzYuyVAZsxl0MRgGTJEmQBFcNTphYh9decYSb74=
 golang.org/x/crypto v0.0.0-20190308221718-c2843e01d9a2/go.mod h1:djNgcEr1/C05ACkg1iLfiJU5Ep61QUkGW8qpdssI0+w=
-golang.org/x/net v0.0.0-20190311183353-d8887717615a/go.mod h1:t9HGtf8HONx5eT2rtn7q6eTqICYqUVnKs3thJo3Qplg=
+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=
+golang.org/x/net v0.0.0-20190620200207-3b0461eec859/go.mod h1:z5CRVTTTmAJ677TzLLGU+0bjPO0LkuOLi4/5GtJWs/s=
+golang.org/x/net v0.0.0-20201021035429-f5854403a974/go.mod h1:sp8m0HH+o8qH0wwXwYZr8TS3Oi6o0r6Gce1SSxlDquU=
+golang.org/x/sync v0.0.0-20190423024810-112230192c58/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM=
+golang.org/x/sync v0.0.0-20201020160332-67f06af15bc9/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM=
 golang.org/x/sys v0.0.0-20190215142949-d0b11bdaac8a/go.mod h1:STP8DvDyc/dI5b8T5hshtkjS+E42TnysNCUPdjciGhY=
-golang.org/x/sys v0.0.0-20190222072716-a9d3bda3a223 h1:DH4skfRX4EBpamg7iV4ZlCpblAHI6s6TDM39bFZumv8=
-golang.org/x/sys v0.0.0-20190222072716-a9d3bda3a223/go.mod h1:STP8DvDyc/dI5b8T5hshtkjS+E42TnysNCUPdjciGhY=
-golang.org/x/text v0.3.0 h1:g61tztE5qeGQ89tm6NTjjM9VPIm088od1l6aSorWRWg=
+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 v0.0.0-20210119212857-b64e53b001e4/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
+golang.org/x/sys v0.0.0-20210216224549-f992740a1bac h1:9glrpwtNjBYgRpb67AZJKHfzj1stG/8BL5H7In2oTC4=
+golang.org/x/sys v0.0.0-20210216224549-f992740a1bac/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
 golang.org/x/text v0.3.0/go.mod h1:NqM8EUOU14njkJ3fqMW+pc6Ldnwhi/IjpwHt7yyuwOQ=
-golang.org/x/tools v0.0.0-20190422233926-fe54fb35175b h1:NVD8gBK33xpdqCaZVVtd6OFJp+3dxkXuz7+U7KaVN6s=
-golang.org/x/tools v0.0.0-20190422233926-fe54fb35175b/go.mod h1:LCzVGOaR6xXOjkQ3onu1FJEFr0SW1gC7cKk1uF8kGRs=
+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 v0.1.0 h1:po9/4sTYwZU9lPhi1tOrb4hCv3qrhiQ77LZfGa2OjwY=
+golang.org/x/tools v0.1.0/go.mod h1:xkSsbof2nBLbhDlRMhhhyNLN/zl3eTqcnHD5viDpcZ0=
+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 v0.0.0-20200804184101-5ec99f83aff1 h1:go1bK/D/BFZV2I8cIQd1NKEZ+0owSTG1fDTci4IqFcE=
+golang.org/x/xerrors v0.0.0-20200804184101-5ec99f83aff1/go.mod h1:I/5z698sn9Ka8TeJc9MKroUUfqBBauWjQqLJ2OPfmY0=
diff --git a/internal/alldeps b/internal/alldeps
index e2ede73..7a7b3f0 100644
--- a/internal/alldeps
+++ b/internal/alldeps
@@ -1,4 +1,7 @@
 github.com/google/subcommands
 github.com/google/wire
 github.com/pmezard/go-difflib
+golang.org/x/mod
+golang.org/x/sys
 golang.org/x/tools
+golang.org/x/xerrors
diff --git a/internal/check_api_change.sh b/internal/check_api_change.sh
index fdbf988..19265ba 100755
--- a/internal/check_api_change.sh
+++ b/internal/check_api_change.sh
@@ -31,23 +31,19 @@ set -euo pipefail
 UPSTREAM_BRANCH="${TRAVIS_BRANCH:-master}"
 echo "Checking for incompatible API changes relative to ${UPSTREAM_BRANCH}..."
 
-INSTALL_DIR="$(mktemp -d)"
 MASTER_CLONE_DIR="$(mktemp -d)"
 PKGINFO_BRANCH=$(mktemp)
 PKGINFO_MASTER=$(mktemp)
 
 function cleanup() {
-  rm -rf "$INSTALL_DIR"
   rm -rf "$MASTER_CLONE_DIR"
   rm -f "$PKGINFO_BRANCH"
   rm -f "$PKGINFO_MASTER"
 }
 trap cleanup EXIT
 
-# Move to a temporary directory while installing apidiff to avoid changing
-# the local .mod file.
-( cd "$INSTALL_DIR" && exec go mod init unused )
-( cd "$INSTALL_DIR" && exec go install golang.org/x/exp/cmd/apidiff )
+# Install apidiff.
+go install golang.org/x/exp/cmd/apidiff@latest
 
 git clone -b "$UPSTREAM_BRANCH" . "$MASTER_CLONE_DIR" &> /dev/null
 
diff --git a/internal/runtests.sh b/internal/runtests.sh
index 2e7915e..75fee90 100755
--- a/internal/runtests.sh
+++ b/internal/runtests.sh
@@ -41,16 +41,26 @@ if [[ "${TRAVIS_OS_NAME:-linux}" != "linux" ]]; then
   exit $result
 fi
 
-echo
-echo "Ensuring .go files are formatted with gofmt -s..."
-mapfile -t go_files < <(find . -name '*.go' -type f | grep -v testdata)
-DIFF="$(gofmt -s -d "${go_files[@]}")"
-if [ -n "$DIFF" ]; then
-  echo "FAIL: please run gofmt -s and commit the result"
-  echo "$DIFF";
-  result=1;
-else
-  echo "OK"
+# Update the regexp below when upgrading to a
+# new Go version. Some checks below we only run
+# for the latest Go version.
+latest_go_version=0
+if [[ $(go version) == *go1\.16* ]]; then
+  latest_go_version=1
+fi
+
+if [[ ${latest_go_version} -eq 1 ]]; then
+  echo
+  echo "Ensuring .go files are formatted with gofmt -s..."
+  mapfile -t go_files < <(find . -name '*.go' -type f | grep -v testdata)
+  DIFF="$(gofmt -s -d "${go_files[@]}")"
+  if [ -n "$DIFF" ]; then
+    echo "FAIL: please run gofmt -s and commit the result"
+    echo "$DIFF";
+    result=1;
+  else
+    echo "OK"
+  fi;
 fi;
 
 
@@ -59,13 +69,13 @@ fi;
 # ./internal/alldeps
 #
 # Whenever project dependencies change, rerun ./internal/listdeps.sh
-if [[ $(go version) == *go1\.12* ]]; then
+if [[ ${latest_go_version} -eq 1 ]]; then
   echo
   echo "Ensuring that there are no dependencies not listed in ./internal/alldeps..."
   (./internal/listdeps.sh | diff ./internal/alldeps - && echo "OK") || {
     echo "FAIL: dependencies changed; run: internal/listdeps.sh > internal/alldeps"
     # Module behavior may differ across versions.
-    echo "using go version 1.12."
+    echo "using the latest go version."
     result=1
   }
 fi
@@ -73,7 +83,7 @@ fi
 
 # For pull requests, check if there are undeclared incompatible API changes.
 # Skip this if we're already going to fail since it is expensive.
-if [[ ${result} -eq 0 ]] && [[ ! -z "${TRAVIS_BRANCH:-x}" ]] && [[ ! -z "${TRAVIS_PULL_REQUEST_SHA:-x}" ]]; then
+if [[ ${latest_go_version} -eq 1 ]] && [[ ${result} -eq 0 ]] && [[ ! -z "${TRAVIS_BRANCH:-x}" ]] && [[ ! -z "${TRAVIS_PULL_REQUEST_SHA:-x}" ]]; then
   echo
   ./internal/check_api_change.sh || result=1;
 fi