diff --git a/.github/workflows/delete-web-preview.yml b/.github/workflows/delete-web-preview.yml
new file mode 100644
index 0000000..6ba1a7e
--- /dev/null
+++ b/.github/workflows/delete-web-preview.yml
@@ -0,0 +1,24 @@
+name: Delete Preview Build
+
+on:
+  pull_request:
+    types: [closed]
+
+permissions:
+  contents: read
+  id-token: write
+  pages: write
+  pull-requests: write
+
+jobs:
+  azure_blob:
+    runs-on: ubuntu-latest
+    env:
+      AZURE_STORAGE_ACCOUNT: measuremaxmature
+      AZURE_STORAGE_SAS_TOKEN: ${{ secrets.AZURE_SAS_TOKEN }}
+      BRANCH_NAME: ${{ github.head_ref || github.ref_name }}
+    steps:
+      - name: Install Azure CLI
+        run: curl -sL https://aka.ms/InstallAzureCLIDeb | sudo bash
+      - name: Delete old blobs
+        run: az storage blob delete-batch -s '$web' --pattern "$BRANCH_NAME/*"
diff --git a/.github/workflows/sphinx.yml b/.github/workflows/sphinx.yml
index e1476d2..a12677f 100644
--- a/.github/workflows/sphinx.yml
+++ b/.github/workflows/sphinx.yml
@@ -5,6 +5,13 @@ on:
     branches: [main]
   pull_request:
 
+# If another web build starts for the same branch, cancel the previous build. This
+# protects us from two builds trying to upload at the same time and clobbering each
+# other.
+concurrency:
+  group: ${{ github.workflow }}-${{ github.ref }}
+  cancel-in-progress: true
+
 permissions:
   contents: read
   pages: write