diff --git a/.travis.yml b/.travis.yml
index 76ac660..51e4a73 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -7,15 +7,22 @@ matrix:
       services:
         - docker
       env: DOCKER_IMAGE=quay.io/pypa/manylinux1_x86_64
+           PLAT=manylinux1_x86_64
     - sudo: required
       services:
         - docker
       env: DOCKER_IMAGE=quay.io/pypa/manylinux1_i686
            PRE_CMD=linux32
+           PLAT=manylinux1_i686
+    - sudo: required
+      services:
+        - docker
+      env: DOCKER_IMAGE=quay.io/pypa/manylinux2010_x86_64
+           PLAT=manylinux2010_x86_64
 
 install:
   - docker pull $DOCKER_IMAGE
 
 script:
-  - docker run --rm -v `pwd`:/io $DOCKER_IMAGE $PRE_CMD /io/travis/build-wheels.sh
+  - docker run --rm -e PLAT=$PLAT -v `pwd`:/io $DOCKER_IMAGE $PRE_CMD /io/travis/build-wheels.sh
   - ls wheelhouse/
diff --git a/README.md b/README.md
index 202c150..988837c 100644
--- a/README.md
+++ b/README.md
@@ -6,17 +6,20 @@ Demo project for building Python wheels for Linux with Travis-CI
 
 
 This is an example of how to use Travis-CI to build
-[PEP 513](https://www.python.org/dev/peps/pep-0513/)-compatible manylinux1
-wheels for Python. It supports both Python 2 and 3 on 32 and 64 bit linux
-architectures.
+[PEP 513](https://www.python.org/dev/peps/pep-0513/)-compatible
+wheels for Python. It supports
 
-Because these wheels need to be compiled on CentOS 5, this example uses Docker
-running on Travis-CI to compile (you don't need to use docker at all to _use_
-these wheels, it's just to compile them). The docker-based build environment
-images are:
+- manylinux1 for both Python 2 and 3 on 32 and 64 bit linux architectures.
+- manylinux2010 for Python 2 and 3 on 64 bit linux architectures.
 
-- 64-bit image (x86-64): ``quay.io/pypa/manylinux1_x86_64`` [![Docker Repository on Quay](https://quay.io/repository/pypa/manylinux1_x86_64/status "Docker Repository on Quay")](https://quay.io/repository/pypa/manylinux1_x86_64)
-- 32-bit image (i686): ``quay.io/pypa/manylinux1_i686`` [![Docker Repository on Quay](https://quay.io/repository/pypa/manylinux1_i686/status "Docker Repository on Quay")](https://quay.io/repository/pypa/manylinux1_i686)
+Because these wheels need to be compiled with a specific toolchain and support
+libraries , this example uses Docker running on Travis-CI to compile (you don't
+need to use docker at all to _use_ these wheels, it's just to compile them).
+The docker-based build environment images are:
+
+- 64-bit image for manylinux1 (x86-64): ``quay.io/pypa/manylinux1_x86_64`` [![Docker Repository on Quay](https://quay.io/repository/pypa/manylinux1_x86_64/status "Docker Repository on Quay")](https://quay.io/repository/pypa/manylinux1_x86_64)
+- 32-bit image for manylinux1 (i686): ``quay.io/pypa/manylinux1_i686`` [![Docker Repository on Quay](https://quay.io/repository/pypa/manylinux1_i686/status "Docker Repository on Quay")](https://quay.io/repository/pypa/manylinux1_i686)
+- 64-bit image for manylinux2010 (x86-64): ``quay.io/pypa/manylinux2010_x86_64`` [![Docker Repository on Quay](https://quay.io/repository/pypa/manylinux2010_x86_64/status "Docker Repository on Quay")](https://quay.io/repository/pypa/manylinux2010_x86_64)
 
 This sample project contains a very simple C compile extension module that links
 to an external library (ATLAS, a linear algebra library). The build is
@@ -31,13 +34,12 @@ resulting build logs can be found at
   https://travis-ci.org/pypa/python-manylinux-demo
 
 The `.travis.yml` file instructs Travis to run the script
-`travis/build-wheels.sh` inside of the 32-bit and 64-bit manylinux1 docker
-build environments. This script builds the package using `pip`. But these
-wheels link against an external library. So to create self-contained wheels,
-the build script runs the wheels through
-[`auditwheel`](https://pypi.python.org/pypi/auditwheel), which copies the external
-library into the wheel itself, so that users won't need to install any extra non-PyPI
-dependencies.
+`travis/build-wheels.sh` inside of the various docker build environments. This
+script builds the package using `pip`. But these wheels link against an
+external library. So to create self-contained wheels, the build script runs the
+wheels through [`auditwheel`](https://pypi.python.org/pypi/auditwheel), which
+copies the external library into the wheel itself, so that users won't need to
+install any extra non-PyPI dependencies.
 
 Code of Conduct
 ---------------
diff --git a/travis/build-wheels.sh b/travis/build-wheels.sh
index e8aa452..e7d48cd 100755
--- a/travis/build-wheels.sh
+++ b/travis/build-wheels.sh
@@ -12,7 +12,7 @@ done
 
 # Bundle external shared libraries into the wheels
 for whl in wheelhouse/*.whl; do
-    auditwheel repair "$whl" -w /io/wheelhouse/
+    auditwheel repair "$whl" --plat $PLAT -w /io/wheelhouse/
 done
 
 # Install packages and test