diff --git a/Dockerfile.test b/Dockerfile.test
index 6985ce70080e7b53eccead0f0ab42e8ed4521092..74dd54cdf2101db0481728915a0c583c575b006e 100644
--- a/Dockerfile.test
+++ b/Dockerfile.test
@@ -1,4 +1,5 @@
-FROM python:2-alpine
+ARG PYTHON_VERSION=2
+FROM python:${PYTHON_VERSION}-alpine
 
 WORKDIR /usr/src/app/
 COPY nginx-ldap-auth-daemon.py /usr/src/app/
diff --git a/t/README b/t/README
index e1248952871553f0134099f89a11797623988681..deff24dd047ed2585982af810a3e52c032cc1f18 100644
--- a/t/README
+++ b/t/README
@@ -1,6 +1,11 @@
 To run tests use supplied Dockerfile.test:
 
-docker build -f Dockerfile.test -t my-tag .
+docker build -f Dockerfile.test -t my-tag
+
+If you desire to use a container with Python3, you can supply an appropriate
+build argument:
+
+docker build -f Dockerfile.test -t my-tag --build-arg PYTHON_VERSION=3 .
 docker run my-tag
 
 To run without Docker:
diff --git a/t/ldap-auth.t b/t/ldap-auth.t
index 22cc20f04c647e481a60072d1386edfce09514fd..5c5648b2599b892b5e4794187a3edbb31a42093c 100644
--- a/t/ldap-auth.t
+++ b/t/ldap-auth.t
@@ -433,7 +433,7 @@ system("ldapadd -H ldap://127.0.0.1:$p5 -x -D \"cn=root,ou=Users,dc=test,dc=loca
 $t->write_file_expand("auth_daemon.sh", <<"EOF");
 AUTHBIN=\$(realpath $AUTHD)
 cd $d
-exec coverage2 run \$AUTHBIN --host 127.0.0.1 \\
+exec coverage run \$AUTHBIN --host 127.0.0.1 \\
     -p %%PORT_8888%% >$d/nginx-ldap-auth-dameon.stdlog 2>&1
 EOF
 
diff --git a/t/runtests.sh b/t/runtests.sh
index 3c23f92446ffb044b0a80ca11db1535ca81bc12b..9950aa35c4d73f8ec19f4cc9ca106456417e5e09 100755
--- a/t/runtests.sh
+++ b/t/runtests.sh
@@ -10,4 +10,4 @@ perl ldap-auth.t
 
 testdir=$(find /tmp -name 'nginx-test-*' -print -quit)
 cd $testdir
-coverage2 html && printf "Coverage report: docker cp <cid>:$testdir/htmlcov <hostdir>\n"
+coverage html && printf "Coverage report: docker cp <cid>:$testdir/htmlcov <hostdir>\n"