diff --git a/.appveyor.yml b/.appveyor.yml
index e0b598c..b5bb25f 100644
--- a/.appveyor.yml
+++ b/.appveyor.yml
@@ -12,8 +12,6 @@ environment:
   global:
       MINGW_32: C:\mingw-w64\i686-6.3.0-posix-dwarf-rt_v5-rev1\mingw32\bin
       MINGW_64: C:\mingw-w64\x86_64-6.3.0-posix-seh-rt_v5-rev1\mingw64\bin
-      OPENBLAS_32: "https://3f23b170c54c2533c070-1c8a9b3114517dc5fe17b7c3f8c63a43.ssl.cf2.rackcdn.com/openblas-v0.3.7-win32-gcc_7_1_0.zip"
-      OPENBLAS_64: "https://3f23b170c54c2533c070-1c8a9b3114517dc5fe17b7c3f8c63a43.ssl.cf2.rackcdn.com/openblas-v0.3.7-win_amd64-gcc_7_1_0.zip"
 
       CYTHON_BUILD_DEP: Cython
       TEST_MODE: fast
@@ -88,33 +86,18 @@ install:
      python -c "import sys,platform,struct;
      print(sys.platform, platform.machine(), struct.calcsize('P') * 8, )"
 
+  # Upgrade to the latest pip, setuptools, and wheel.
+  - python -m pip install -U pip setuptools wheel urllib3
+
   # Download and install static "openblas.a" to PYTHON\lib
   - ps: |
-      $PYTHON_ARCH = $env:PYTHON_ARCH
       $PYTHON = $env:PYTHON
-      If ($PYTHON_ARCH -eq 32) {
-          $OPENBLAS = $env:OPENBLAS_32
-      } Else {
-          $OPENBLAS = $env:OPENBLAS_64
-      }
-      $clnt = new-object System.Net.WebClient
-      $file = "$(New-TemporaryFile).zip"
-      $tmpdir = New-TemporaryFile | %{ rm $_; mkdir $_ }
+      $lib = python numpy/tools/openblas_support.py
       $destination = "$PYTHON\lib\openblas.a"
-      echo $file
-      echo $tmpdir
-      echo $OPENBLAS
-      $clnt.DownloadFile($OPENBLAS,$file)
-      Expand-Archive $file $tmpdir
-      rm $tmpdir\$PYTHON_ARCH\lib\*.dll.a
-      $lib = ls $tmpdir\$PYTHON_ARCH\lib\*.a | ForEach { ls $_ } | Select-Object -first 1
       echo $lib
       cp $lib $destination
       ls $destination
 
-  # Upgrade to the latest pip, setuptools, and wheel.
-  - python -m pip install -U pip setuptools wheel
-
   # Install build requirements.
   - pip install "%CYTHON_BUILD_DEP%" --install-option="--no-cython-compile"
 
diff --git a/.travis.yml b/.travis.yml
index 9ef3739..fcf26e3 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -5,8 +5,6 @@ env:
         - BUILD_COMMIT=e94cec800304a6a467cf90ce4e7d3e207770b4b4
         - BUILD_DEPENDS=cython
         - TEST_DEPENDS="pytest hypothesis"
-        - PLAT=x86_64
-        - UNICODE_WIDTH=32
         - WHEELHOUSE_UPLOADER_USERNAME=travis-worker
         # Following generated with
         # travis encrypt -r MacPython/numpy-wheels WHEELHOUSE_UPLOADER_SECRET=<the api key>
@@ -17,44 +15,48 @@ env:
         - EXTRA_ARGV="'--disable-pytest-warnings'"
 
 language: python
-# Default Python version is usually 2.7
-python: 3.6
-sudo: required
 dist: bionic
 services: docker
+os: linux
 
-matrix:
-  exclude:
-      # Exclude the default Python 3.6 build
-      - python: 3.6
+jobs:
   include:
     - os: linux
       env:
         - MB_PYTHON_VERSION=3.6
         - MB_ML_VER=2010
+        - PLAT=x86_64
     - os: linux
       env:
         - MB_PYTHON_VERSION=3.6
         - MB_ML_VER=2010
         - PLAT=i686
+        - ENV_VARS_PATH=env_vars_32.sh
+        - DOCKER_TEST_IMAGE=multibuild/xenial_{PLAT}
     - os: linux
       env:
         - MB_PYTHON_VERSION=3.7
         - MB_ML_VER=2010
+        - PLAT=x86_64
     - os: linux
       env:
         - MB_PYTHON_VERSION=3.7
         - MB_ML_VER=2010
         - PLAT=i686
+        - ENV_VARS_PATH=env_vars_32.sh
+        - DOCKER_TEST_IMAGE=multibuild/xenial_{PLAT}
     - os: linux
       env:
         - MB_PYTHON_VERSION=3.8
         - MB_ML_VER=2010
+        - PLAT=x86_64
     - os: linux
       env:
         - MB_PYTHON_VERSION=3.8
         - MB_ML_VER=2010
         - PLAT=i686
+        - ENV_VARS_PATH=env_vars_32.sh
+        - DOCKER_TEST_IMAGE=multibuild/xenial_{PLAT}
     - os: osx
       language: generic
       osx_image: xcode10.1
diff --git a/README.rst b/README.rst
index 6c71b8e..d788105 100644
--- a/README.rst
+++ b/README.rst
@@ -19,10 +19,12 @@ How it works
 
 The wheel-building repository:
 
-* does a fresh build of any required C / C++ libraries;
-* builds a numpy wheel, linking against these fresh builds;
+* checks out either a known version of NumPy or master's HEAD
+* downloads OpenBLAS using numpy/tools/openblas_support.py
+* builds a numpy wheel, linking against the downloaded library and using
+  the appropriate additional variables from `env_vars.sh` or `env_vars32.sh`
 * processes the wheel using delocate_ (OSX) or auditwheel_ ``repair``
-  (Manylinux1_).  ``delocate`` and ``auditwheel`` copy the required dynamic
+  (manylinux_).  ``delocate`` and ``auditwheel`` copy the required dynamic
   libraries into the wheel and relinks the extension modules against the
   copied libraries;
 * uploads the built wheels to http://wheels.scipy.org (a Rackspace container
@@ -30,7 +32,7 @@ The wheel-building repository:
 
 The resulting wheels are therefore self-contained and do not need any external
 dynamic libraries apart from those provided as standard by OSX / Linux as
-defined by the manylinux1 standard.
+defined by the manylinux standard.
 
 The ``.travis.yml`` file in this repository has a line containing the API key
 for the Rackspace container encrypted with an RSA key that is unique to the
@@ -132,7 +134,7 @@ upload them to PyPI.
 
 Of course, you will need permissions to upload to PyPI, for this to work.
 
-.. _manylinux1: https://www.python.org/dev/peps/pep-0513
+.. _manylinux: https://www.python.org/dev/peps/pep-0513
 .. _twine: https://pypi.python.org/pypi/twine
 .. _bs4: https://pypi.python.org/pypi/beautifulsoup4
 .. _delocate: https://pypi.python.org/pypi/delocate
diff --git a/config.sh b/config.sh
index 0329262..e515500 100644
--- a/config.sh
+++ b/config.sh
@@ -7,6 +7,9 @@ function build_wheel {
     local lib_plat=$PLAT
     if [ -n "$IS_OSX" ]; then
         install_gfortran
+    else
+        # For manylinux2010 builds with manylinux1 openblas builds
+        $use_sudo yum install -y libgfortran-4.4.7
     fi
     build_libs $lib_plat
     # Fix version error for development wheels by using bdist_wheel
@@ -14,37 +17,32 @@ function build_wheel {
 }
 
 function build_libs {
-    local plat=${1:-$PLAT}
-    # Force 64-bit OpenBLAS library for macOS intel (dual arch)
-    # builds. For these builds, we pretend to be dual arch, but in
-    # fact we're only using the 64-bit build of OpenBLAS
-    if [ -n $IS_OSX ] && [ $plat == intel ]; then
-        plat=x86_64
-    fi
-    local tar_fname=$(get_gf_lib "openblas-${OPENBLAS_VERSION}" "$plat")
-    local tar_path=$(abspath $tar_fname)
-    # Sudo needed for macOS
-    local use_sudo=""
-    [ -n "$IS_OSX" ] && use_sudo="sudo"
-    (cd / && $use_sudo tar zxf $tar_path)
+    # Use the same incantation as numpy/tools/travis-before-install.sh to
+    # download and un-tar the openblas libraries. The python call returns
+    # the un-tar root directory, then the files are copied into /usr/local.
+    # Could utilize a site.cfg instead to prevent the copy.
+    python -mpip install urllib3
+    basedir=$(python numpy/tools/openblas_support.py)
+    $use_sudo cp -r $basedir/lib/* /usr/local/lib
+    $use_sudo cp $basedir/include/* /usr/local/include
 }
 
 function get_test_cmd {
     local extra_argv=${1:-$EXTRA_ARGV}
     echo "import sys; import numpy; \
         sys.exit(not numpy.test('full', \
-        extra_argv=[${extra_argv}]))"
+        extra_argv=['-vv', ${extra_argv}]))"
 }
 
 function run_tests {
     # Runs tests on installed distribution from an empty directory
-    # We only run the 64 bit tests as of NumPy 1.16.
     if [ -z "$IS_OSX" ]; then
         apt-get -y update && apt-get install -y gfortran
     fi
     python -c "$(get_test_cmd)"
     # Check bundled license file
     python ../check_license.py
-    # Show BLAS / LAPACK used
+    # Show BLAS / LAPACK used. Since this uses a wheel we cannot use
+    # tools/openblas_config.py; tools is not part of what is shipped
     python -c 'import numpy; numpy.show_config()'
 }
diff --git a/env_vars_32.sh b/env_vars_32.sh
new file mode 100644
index 0000000..46b1aaa
--- /dev/null
+++ b/env_vars_32.sh
@@ -0,0 +1,6 @@
+# Environment variables for 32-bit build.
+# The important difference from the 64-bit build is `-msse2` to
+# compile sse loops for ufuncs.
+OPENBLAS_VERSION="v0.3.7"
+MACOSX_DEPLOYMENT_TARGET=10.9
+CFLAGS="-msse2 -std=c99 -fno-strict-aliasing"
diff --git a/gfortran-install b/gfortran-install
index e9764d0..d430fe6 160000
--- a/gfortran-install
+++ b/gfortran-install
@@ -1 +1 @@
-Subproject commit e9764d0a8f4e3adcd385c319e7742177193484c7
+Subproject commit d430fe6e38b6c5149c53f775a4437964e2f7b883
diff --git a/multibuild b/multibuild
index 0c4a992..3bd75ee 160000
--- a/multibuild
+++ b/multibuild
@@ -1 +1 @@
-Subproject commit 0c4a9920fa4635419fcea61f10d6dc0cd50e3639
+Subproject commit 3bd75eee8fa98ee70e29d59f4ec5a15291362cc2
diff --git a/numpy b/numpy
index 9e419a0..f1a247f 160000
--- a/numpy
+++ b/numpy
@@ -1 +1 @@
-Subproject commit 9e419a0359cb5dbb9ae0b2711ab7a59b121a98cf
+Subproject commit f1a247f9952085db72c3f8248f8336a0961d825c