diff --git a/.github/workflows/bwrap.yml b/.github/workflows/bwrap.yml
index 66cea846..ee484472 100644
--- a/.github/workflows/bwrap.yml
+++ b/.github/workflows/bwrap.yml
@@ -2,7 +2,7 @@
 #
 # SPDX-License-Identifier: GPL-3.0-or-later
 
-name: Run under bubblewrap
+name: Run under (bubble)wrap
 
 on:
   workflow_dispatch:
@@ -13,10 +13,15 @@ on:
 
 jobs:
   pass1:
-    name: Run up to Linux build under bubblewrap
+    name: Run up to Linux build under (bubble)wrap
     runs-on: ubuntu-latest
+    strategy:
+      fail-fast: true
+      matrix:
+        virt-tool: [bwrap, wrap]
     steps:
       - name: Install bubblewrap
+        if: matrix.virt-tool == 'bwrap'
         run: sudo apt install bubblewrap
       - name: Checkout repo
         uses: actions/checkout@v3
@@ -43,7 +48,7 @@ jobs:
             distfiles
           key: cache-${{ hashFiles('steps/*/sources') }}
       - name: Run bootstrap
-        run: ./rootfs.py --bwrap --external-sources --build-kernels --cores 2 --internal-ci pass1
+        run: ./rootfs.py --${{matrix.virt-tool}} --external-sources --build-kernels --cores 2 --internal-ci pass1
       - name: Archive created packages
         if: failure() # archive failed builds progress
         uses: actions/upload-artifact@v3
@@ -56,14 +61,19 @@ jobs:
         uses: actions/upload-artifact@v3
         with:
           name: internal_pass1_image
-          path: pass1_image.tar
+          path: pass1_image_${{matrix.virt-tool}}.tar
 
   pass2:
-    name: Run up to Python bootstrap under bubblewrap
+    name: Run up to Python bootstrap under (bubble)wrap
     needs: pass1
     runs-on: ubuntu-latest
+    strategy:
+      fail-fast: true
+      matrix:
+        virt-tool: [bwrap, wrap]
     steps:
       - name: Install bubblewrap
+        if: matrix.virt-tool == 'bwrap'
         run: sudo apt install bubblewrap
       - name: Checkout repo
         uses: actions/checkout@v3
@@ -77,7 +87,7 @@ jobs:
         with:
           name: internal_pass1_image
       - name: Extract pass1_image
-        run: tar -xf pass1_image.tar
+        run: tar -xf pass1_image_${{matrix.virt-tool}}.tar
       - name: Query cache for sources
         id: cache
         uses: actions/cache/restore@v3
@@ -96,7 +106,7 @@ jobs:
             distfiles
           key: cache-${{ hashFiles('steps/*/sources') }}
       - name: Run bootstrap
-        run: ./rootfs.py --bwrap --external-sources --build-kernels --cores 2 --internal-ci pass2
+        run: ./rootfs.py --${{matrix.virt-tool}} --external-sources --build-kernels --cores 2 --internal-ci pass2
       - name: Archive created packages
         if: failure() # archive failed builds progress
         uses: actions/upload-artifact@v3
@@ -109,14 +119,19 @@ jobs:
         uses: actions/upload-artifact@v3
         with:
           name: internal_pass2_image
-          path: pass2_image.tar
+          path: pass2_image_${{matrix.virt-tool}}.tar
 
   pass3:
-    name: Run remaining builds under bubblewrap
+    name: Run remaining builds under (bubble)wrap
     needs: pass2
     runs-on: ubuntu-latest
+    strategy:
+      fail-fast: true
+      matrix:
+        virt-tool: [bwrap, wrap]
     steps:
       - name: Install bubblewrap
+        if: matrix.virt-tool == 'bwrap'
         run: sudo apt install bubblewrap
       - name: Checkout repo
         uses: actions/checkout@v3
@@ -130,7 +145,7 @@ jobs:
         with:
           name: internal_pass2_image
       - name: Extract pass2_image
-        run: tar -xf pass2_image.tar
+        run: tar -xf pass2_image_${{matrix.virt-tool}}.tar
       - name: Query cache for sources
         id: cache
         uses: actions/cache/restore@v3
@@ -149,10 +164,10 @@ jobs:
             distfiles
           key: cache-${{ hashFiles('steps/*/sources') }}
       - name: Run bootstrap
-        run: ./rootfs.py --bwrap --external-sources --build-kernels --cores 2 --internal-ci pass3
+        run: ./rootfs.py --${{matrix.virt-tool}} --external-sources --build-kernels --cores 2 --internal-ci pass3
       - name: Archive created packages
         if: always() # archive both failed and successful builds
         uses: actions/upload-artifact@v3
         with:
-          name: packages
+          name: packages_${{matrix.virt-tool}}
           path: target/external/repo/**