diff --git a/.github/workflows/wheel.yaml b/.github/workflows/wheel.yaml
index cebd52c9..406b3473 100644
--- a/.github/workflows/wheel.yaml
+++ b/.github/workflows/wheel.yaml
@@ -6,9 +6,21 @@ concurrency:
   group: ${{ github.workflow }}-${{ github.ref }}
   cancel-in-progress: true
 
+env:
+  # Build all wheels on either:
+  #    - tagged release
+  #    - pull request opened with "test all wheels" label
+  #    - pull requests when "test all wheels" label is added
+  BUILD_ALL: |
+    ${{
+        (github.event_name == 'push' && startsWith(github.event.ref, 'refs/tags/v'))
+        || contains(github.event.pull_request.labels.*.name, 'test all wheels')
+        || (github.event.action == 'labeled' && github.event.label.name == 'test all wheels')
+    }}
+
 jobs:
   build_wheels:
-    name: Build wheel on ${{ matrix.os }}
+    name: Build wheels on ${{ matrix.os }}
     runs-on: ${{ matrix.os }}
     strategy:
       fail-fast: false
@@ -18,7 +30,9 @@ jobs:
     env:
       CIBW_TEST_COMMAND: python -c "import numcodecs"
       CIBW_BUILD: "cp310-* cp311-* cp312-* cp313-*"
-      CIBW_SKIP: "pp* *-musllinux_* *win32 *_i686 *_s390x"
+      CIBW_ARCHS_MACOS: native
+      CIBW_ARCHS_WINDOWS: native
+      CIBW_ARCHS_LINUX: "x86_64 aarch64"
       # note: CIBW_ENVIRONMENT is now set in pyproject.toml
 
     steps:
@@ -26,6 +40,15 @@ jobs:
         with:
           submodules: true
 
+      - name: Restrict number of wheel builds on PRs
+        if: ${{ !env.BUILD_ALL }}
+        run: |
+          echo "CIBW_BUILD=cp310-win_amd64 cp311-manylinux_x86_64 cp312-macosx_x86_64 cp312-macosx_arm64" >> $GITHUB_ENV
+
+      - name: Set up QEMU
+        if: ${{ matrix.os == 'ubuntu-latest' }}
+        uses: docker/setup-qemu-action@v3
+
       - uses: pypa/cibuildwheel@v2.21.2
 
       - uses: actions/upload-artifact@v4
diff --git a/docs/release.rst b/docs/release.rst
index 434c811f..1a1dbec9 100644
--- a/docs/release.rst
+++ b/docs/release.rst
@@ -25,6 +25,8 @@ Enhancements
 * Update bundled c-blosc to v1.26.1. This updates Zlib to v1.3.1
   and Zstd to v1.5.6.
   By :user:`David Stansby <dstansby>`, :issue:`560`.
+* Build aarch64 wheels on linuxL
+  By :user:`David Stansby <dstansby>`, :issue:`531`
 
 Fix
 ~~~
@@ -38,6 +40,13 @@ Maintenance
 * Remove pin on Sphinx
   By :user:`Elliott Sales de Andrade <QuLogic>`, :issue:`552`.
 
+* Restrict the number of wheels built on pull requests.
+  By :user:`David Stansby <dstansby>`, :issue:`531`
+
+* Add an option to build all wheels on pull requests by adding
+  the 'build all wheels' label.
+  By :user:`David Stansby <dstansby>`, :issue:`531`
+
 
 .. _release_0.13.0:
 
diff --git a/setup.py b/setup.py
index 815224aa..9f71d696 100644
--- a/setup.py
+++ b/setup.py
@@ -24,7 +24,9 @@
 if have_cflags:
     # respect compiler options set by user
     pass
-elif os.name == 'posix':
+elif os.name == 'posix' and os.uname()[4] != 'aarch64':
+    # These flags aren't recognised by gcc on aarch64
+    # (at least when we build the aarch64 wheens on GitHub actions)
     if disable_sse2:
         base_compile_args.append('-mno-sse2')
     elif have_sse2: