diff --git a/.github/workflows/dist.yml b/.github/workflows/dist.yml
index c77c1783f9d..c5676b64787 100644
--- a/.github/workflows/dist.yml
+++ b/.github/workflows/dist.yml
@@ -45,7 +45,7 @@ jobs:
       - name: make download (--disable-download-from-upstream-url)
         id: make_download
         run: |
-          make -k download
+          make -k download DOWNLOAD_PACKAGES=":all: --no-file huge"
         env:
           MAKE: make -j8
       - name: Reconfigure with --enable-download-from-upstream-url
@@ -61,9 +61,13 @@ jobs:
       - name: make download (--enable-download-from-upstream-url)
         if: (success() || failure()) && steps.make_download.outcome != 'success'
         run: |
-          make -k download
+          make -k download DOWNLOAD_PACKAGES=":all: --no-file huge"
         env:
           MAKE: make -j8
+      - name: Remove what cannot be distributed
+        if: success() || failure()
+        run: |
+          rm -f upstream/*do-not-distribute*
       - uses: actions/upload-artifact@v3
         if: success() || failure()
         with:
diff --git a/Makefile b/Makefile
index 56e11c69f50..6964770bd02 100644
--- a/Makefile
+++ b/Makefile
@@ -87,10 +87,11 @@ buildbot-python3:
 	$(MAKE)
 
 # Preemptively download all source tarballs of normal packages.
+DOWNLOAD_PACKAGES=:all:
 download:
 	export SAGE_ROOT=$$(pwd) && \
 	export PATH=$$SAGE_ROOT/build/bin:$$PATH && \
-	sage-package download :all:
+	sage-package download $(DOWNLOAD_PACKAGES)
 
 dist: build/make/Makefile
 	./sage --sdist