diff --git a/.github/workflows/build.yml b/.github/workflows/build.yml
index 89ed87ecf91..5242dfc06f9 100644
--- a/.github/workflows/build.yml
+++ b/.github/workflows/build.yml
@@ -85,20 +85,19 @@ jobs:
             (cd worktree-image && git commit -q -m "current changes" --allow-empty -a && git am; git reset --quiet old; git add -N .) < upstream/ci_fixes.patch
           fi
 
-      - name: Incremental build, test changed files (sage -t --new)
+      - name: Incremental build
         id: incremental
         run: |
           # Now re-bootstrap and build. The build is incremental because we were careful with the timestamps.
-          # We run tests with "sage -t --new"; this only tests the uncommitted changes.
-          ./bootstrap && make build && ./sage -t --new -p2
+          ./bootstrap && make build
         working-directory: ./worktree-image
         env:
           MAKE: make -j2 --output-sync=recurse
           SAGE_NUM_THREADS: 2
 
-      - name: Build and test modularized distributions
+      - name: Build modularized distributions
         if: always() && steps.worktree.outcome == 'success'
-        run: make V=0 tox && make pypi-wheels
+        run: make V=0 tox && make SAGE_CHECK=no pypi-wheels
         working-directory: ./worktree-image
         env:
           MAKE: make -j2 --output-sync=recurse
@@ -143,6 +142,26 @@ jobs:
           MAKE: make -j2 --output-sync=recurse
           SAGE_NUM_THREADS: 2
 
+      # Testing
+
+      - name: Test changed files (sage -t --new)
+        if: always() && steps.build.outcome == 'success'
+        run: |
+          # We run tests with "sage -t --new"; this only tests the uncommitted changes.
+          ./sage -t --new -p2
+        working-directory: ./worktree-image
+        env:
+          MAKE: make -j2 --output-sync=recurse
+          SAGE_NUM_THREADS: 2
+
+      - name: Test modularized distributions
+        if: always() && steps.build.outcome == 'success'
+        run: make V=0 tox && make pypi-wheels-check
+        working-directory: ./worktree-image
+        env:
+          MAKE: make -j2 --output-sync=recurse
+          SAGE_NUM_THREADS: 2
+
       - name: Pytest
         if: contains(github.ref, 'pytest')
         run: |
diff --git a/build/bin/sage-dist-helpers b/build/bin/sage-dist-helpers
index 67a2201d31f..73119347438 100644
--- a/build/bin/sage-dist-helpers
+++ b/build/bin/sage-dist-helpers
@@ -321,7 +321,15 @@ sdh_store_wheel() {
     mkdir -p "${SAGE_DESTDIR}${SAGE_SPKG_WHEELS}" && \
         $sudo mv "$wheel" "${SAGE_DESTDIR}${SAGE_SPKG_WHEELS}/" || \
         sdh_die "Error storing $wheel"
-    wheel="${SAGE_DESTDIR}${SAGE_SPKG_WHEELS}/${wheel##*/}"
+    wheel="${SAGE_SPKG_WHEELS}/${wheel##*/}"
+    if [ -n "${SAGE_SPKG_SCRIPTS}" -a -n "${PKG_BASE}" ]; then
+        wheel_basename="${wheel##*/}"
+        distname="${wheel_basename%%-*}"
+        # Record name and wheel file location
+        mkdir -p ${SAGE_DESTDIR}${SAGE_SPKG_SCRIPTS}/${PKG_BASE}
+        echo "${distname} @ file://${wheel}" >> ${SAGE_DESTDIR}${SAGE_SPKG_SCRIPTS}/${PKG_BASE}/spkg-requirements.txt
+    fi
+    wheel="${SAGE_DESTDIR}${wheel}"
 }
 
 sdh_store_and_pip_install_wheel() {
@@ -373,11 +381,6 @@ sdh_store_and_pip_install_wheel() {
     fi
     $sudo sage-pip-install $root $pip_options "$wheel" || \
         sdh_die "Error installing ${wheel##*/}"
-    if [ -n "${SAGE_PKG_DIR}" ]; then
-        # Record name of installed distribution name for uninstallation.
-        wheel=${wheel##*/}
-        echo "${wheel%%-*}" >> ${SAGE_PKG_DIR}/spkg-piprm-requirements.txt
-    fi
 }
 
 sdh_pip_uninstall() {
diff --git a/build/bin/sage-spkg b/build/bin/sage-spkg
index 9b38ed6afc7..b540c8e866f 100755
--- a/build/bin/sage-spkg
+++ b/build/bin/sage-spkg
@@ -548,7 +548,7 @@ WRAPPED_SCRIPTS="build install check preinst postinst $INSTALLED_SCRIPTS"
 
 # Prepare script for uninstallation of packages that use sdh_pip_install
 # or sdh_store_and_pip_install_wheel.
-echo 'sdh_pip_uninstall -r $SAGE_SPKG_SCRIPTS/$PKG_BASE/spkg-piprm-requirements.txt' > spkg-piprm.in
+echo 'sdh_pip_uninstall -r $SAGE_SPKG_SCRIPTS/$PKG_BASE/spkg-requirements.txt' > spkg-piprm.in
 
 for script in $WRAPPED_SCRIPTS; do
     # 'Installed' scripts are not run immediately out of the package build
@@ -567,24 +567,6 @@ for script in $WRAPPED_SCRIPTS; do
     fi
 done
 
-
-# When there is no spkg-install, assume the "spkg" is a tarball not
-# specifically made for Sage.  Since we want it to be as easy as
-# possible to install such a package, we "guess" spkg-install.
-if [ ! -f spkg-install ]; then
-    echo '#!/usr/bin/env bash' > spkg-install
-    if [ -x configure ]; then
-        echo './configure --prefix="$SAGE_INST_LOCAL" && make && $SAGE_SUDO make install' >> spkg-install
-    elif [ -f setup.py ]; then
-        echo 'python setup.py install' >> spkg-install
-    else
-        echo >&2 "Error: There is no spkg-install script, no setup.py, and no configure"
-        echo >&2 "script, so I do not know how to install $PKG_SRC."
-        exit 1
-    fi
-    chmod +x spkg-install
-fi
-
 echo "****************************************************"
 echo "Host system:"
 uname -a
@@ -722,9 +704,7 @@ unset SAGE_DESTDIR_LOCAL
 # removed by sage-spkg-uninstall
 INSTALLED_SCRIPTS_DEST="$SAGE_SPKG_SCRIPTS/$PKG_BASE"
 
-if [ -f spkg-piprm-requirements.txt ]; then
-    INSTALLED_SCRIPTS="$INSTALLED_SCRIPTS piprm-requirements.txt"
-else
+if [ ! -f $INSTALLED_SCRIPTS_DEST/spkg-requirements.txt ]; then
     # No packages to uninstall with pip, so remove the prepared uninstall script
     rm -f spkg-piprm spkg-piprm.in
 fi
diff --git a/build/make/Makefile.in b/build/make/Makefile.in
index cc004d08c3c..6031ae7fa2a 100644
--- a/build/make/Makefile.in
+++ b/build/make/Makefile.in
@@ -468,6 +468,8 @@ wheels:
 	$(MAKE_REC) SAGE_EDITABLE=no SAGE_WHEELS=yes $(WHEEL_PACKAGES)
 	@echo "Built wheels are in venv/var/lib/sage/wheels/"
 
+pypi-wheels-check: $(PYPI_WHEEL_PACKAGES:%=%-check)
+
 #==============================================================================
 # Setting SAGE_CHECK... variables
 #==============================================================================
@@ -724,15 +726,21 @@ $(1)-$(4)-no-deps:
 	    echo "$$($(4)_DISABLED_MESSAGE)" 2>&1; \
 	    exit 1; \
 	elif [ -x '$$(SAGE_ROOT)/build/pkgs/$(1)/spkg-install' ]; then \
+	    rm -rf '$$($(4))/var/lib/sage/scripts/$(1)'; \
 	    cd '$$(SAGE_ROOT)/build/pkgs/$(1)' && \
 		. '$$(SAGE_ROOT)/src/bin/sage-src-env-config' && \
 		. '$$(SAGE_ROOT)/src/bin/sage-env-config' && \
 		. '$$(SAGE_ROOT)/src/bin/sage-env' && \
 		. '$$(SAGE_ROOT)/build/bin/sage-build-env-config' && \
 		. '$$(SAGE_ROOT)/build/bin/sage-build-env' && \
+		PKG_BASE="$(1)" \
+		PKG_VER="$(2)" \
+		PKG_NAME="$(1)-$(2)" \
 		SAGE_SPKG_WHEELS=$$($(4))/var/lib/sage/wheels \
+		SAGE_SPKG_SCRIPTS=$$($(4))/var/lib/sage/scripts \
 		SAGE_INST_LOCAL=$$($(4)) \
-		sage-logger -p 'SAGE_CHECK=$$(SAGE_CHECK_$(1)) $$(SAGE_ROOT)/build/pkgs/$(1)/spkg-install' '$$(SAGE_LOGS)/$(1)-$(2).log' && \
+		SAGE_CHECK=$$(SAGE_CHECK_$(1)) \
+		sage-logger -p '$$(SAGE_ROOT)/build/pkgs/$(1)/spkg-install && if [ $$$$SAGE_CHECK != no -a -x $$(SAGE_ROOT)/build/pkgs/$(1)/spkg-check ]; then $$(SAGE_ROOT)/build/pkgs/$(1)/spkg-check; fi' '$$(SAGE_LOGS)/$(1)-$(2).log' && \
 	    rm -f "$$($(4))/$(SPKG_INST_RELDIR)/$(1)"-* && \
 	    touch "$$($(4))/$(SPKG_INST_RELDIR)/$(1)-$(2)"; \
 	else ( \
@@ -752,6 +760,26 @@ $(1)-$(4)-no-deps:
 
 $(1)-no-deps: $(1)-$(4)-no-deps
 
+$(1)-$(4)-check:
+	$(PLUS)@if [ -x $$(SAGE_ROOT)/build/pkgs/$(1)/spkg-check ]; then \
+	    cd '$$(SAGE_ROOT)/build/pkgs/$(1)' && \
+		. '$$(SAGE_ROOT)/src/bin/sage-src-env-config' && \
+		. '$$(SAGE_ROOT)/src/bin/sage-env-config' && \
+		. '$$(SAGE_ROOT)/src/bin/sage-env' && \
+		. '$$(SAGE_ROOT)/build/bin/sage-build-env-config' && \
+		. '$$(SAGE_ROOT)/build/bin/sage-build-env' && \
+		PKG_BASE="$(1)" \
+		PKG_VER="$(2)" \
+		PKG_NAME="$(1)-$(2)" \
+		SAGE_SPKG_WHEELS=$$($(4))/var/lib/sage/wheels \
+		SAGE_SPKG_SCRIPTS=$$($(4))/var/lib/sage/scripts \
+		SAGE_INST_LOCAL=$$($(4)) \
+		SAGE_CHECK=$$(SAGE_CHECK_$(1)) \
+		sage-logger -p '$$(SAGE_ROOT)/build/pkgs/$(1)/spkg-check' '$$(SAGE_LOGS)/$(1)-$(2).log'; \
+	    fi
+
+$(1)-check: $(1)-$(4)-check
+
 $(1)-$(4)-uninstall:
 	-$(AM_V_at)cd '$$(SAGE_ROOT)/build/pkgs/$(1)' && \
 		. '$$(SAGE_ROOT)/src/bin/sage-src-env-config' && \
diff --git a/build/pkgs/sage_sws2rst/spkg-check b/build/pkgs/sage_sws2rst/spkg-check
index 667df773214..7372750871e 100755
--- a/build/pkgs/sage_sws2rst/spkg-check
+++ b/build/pkgs/sage_sws2rst/spkg-check
@@ -1,2 +1,11 @@
 #! /bin/sh
-cd src && ./check.sh
+cd src
+./check.sh
+if [ $? -ne 0 ]; then
+    if [ "$SAGE_CHECK" = "warn" ]; then
+        echo >&2 "Warning: Failures testing package $PKG_NAME (ignored)"
+    else
+        echo >&2 "Error testing package $PKG_NAME"
+        exit 1
+    fi
+fi
diff --git a/build/pkgs/sage_sws2rst/spkg-install b/build/pkgs/sage_sws2rst/spkg-install
index 9cb71471fd8..a180fb36542 100755
--- a/build/pkgs/sage_sws2rst/spkg-install
+++ b/build/pkgs/sage_sws2rst/spkg-install
@@ -18,13 +18,3 @@ if [ "$SAGE_EDITABLE" = yes ]; then
 else
     sdh_pip_install .
 fi
-cd ..
-# For type=script packages, spkg-check is not run
-case "$SAGE_CHECK" in
-    yes)
-        ./spkg-check
-        ;;
-    warn)
-        ./spkg-check || echo >&2  "Warning: Failures testing package sage_sws2rst (ignored)"
-        ;;
-esac
diff --git a/build/pkgs/sagemath_categories/spkg-check b/build/pkgs/sagemath_categories/spkg-check
new file mode 120000
index 00000000000..91c6b1835fc
--- /dev/null
+++ b/build/pkgs/sagemath_categories/spkg-check
@@ -0,0 +1 @@
+../sagemath_objects/spkg-check
\ No newline at end of file
diff --git a/build/pkgs/sagemath_environment/spkg-check b/build/pkgs/sagemath_environment/spkg-check
new file mode 120000
index 00000000000..91c6b1835fc
--- /dev/null
+++ b/build/pkgs/sagemath_environment/spkg-check
@@ -0,0 +1 @@
+../sagemath_objects/spkg-check
\ No newline at end of file
diff --git a/build/pkgs/sagemath_objects/spkg-check b/build/pkgs/sagemath_objects/spkg-check
new file mode 100755
index 00000000000..87cea0fc38f
--- /dev/null
+++ b/build/pkgs/sagemath_objects/spkg-check
@@ -0,0 +1,27 @@
+#!/usr/bin/env bash
+cd src
+
+export PIP_NO_INDEX=true
+export PIP_FIND_LINKS="file://$SAGE_SPKG_WHEELS"
+
+export TOX_PARALLEL_NO_SPINNER=1
+wheel="$(sed -n '1s,.*@ file://,,p' $SAGE_SPKG_SCRIPTS/$PKG_BASE/spkg-requirements.txt)"
+echo Running "tox -r -p auto -v --installpkg $wheel"
+tox -r -p auto -v --installpkg "$wheel"
+status=$?
+case $status:$SAGE_CHECK:$([ -r known-test-failures.json ]; echo $?) in
+    0:*:0)    echo "Passed the test suite (modulo baseline known-test-failures*.json)";;
+    0:*:*)    echo "Passed the test suite";;
+    *:warn:0) echo "Warning: New failures (not in baseline known-test-failures*.json (ignored)"; status=0;;
+    *:warn:*) echo "Warning: Failures testing the package (ignored)"; status=0;;
+    *:yes:0)  echo "New failures, not in baseline known-test-failures*.json";;
+    *:yes:*)  echo "Failures testing the package";;
+esac
+# Show summaries of failures (suppress lines ending with '[failed in baseline]')
+for f in $(pwd)/.tox/sagepython-sagewheels-nopypi-norequirements*/log/*-command*.log; do
+    if [ -r "$f" ]; then
+        echo "$f"
+        grep '^sage -t.*#[^]]*$' "$f"
+    fi
+done
+exit $status
diff --git a/build/pkgs/sagemath_objects/spkg-install b/build/pkgs/sagemath_objects/spkg-install
index 472e7f0d4d6..18ceb18724d 100755
--- a/build/pkgs/sagemath_objects/spkg-install
+++ b/build/pkgs/sagemath_objects/spkg-install
@@ -23,26 +23,3 @@ python3 -m build --outdir "$DIST_DIR"/dist . || sdh_die "Failure building sdist
 
 wheel=$(cd "$DIST_DIR" && sdh_store_wheel . >&2 && echo $wheel)
 ls -l "$wheel"
-
-if [ "$SAGE_CHECK" != no ]; then
-    export TOX_PARALLEL_NO_SPINNER=1
-    echo Running "tox -r -p auto -v --installpkg $wheel"
-    tox -r -p auto -v --installpkg $wheel
-    status=$?
-    case $status:$SAGE_CHECK:$([ -r known-test-failures.json ]; echo $?) in
-        0:*:0)    echo "Passed the test suite (modulo baseline known-test-failures*.json)";;
-        0:*:*)    echo "Passed the test suite";;
-        *:warn:0) echo "Warning: New failures (not in baseline known-test-failures*.json (ignored)"; status=0;;
-        *:warn:*) echo "Warning: Failures testing the package (ignored)"; status=0;;
-        *:yes:0)  echo "New failures, not in baseline known-test-failures*.json";;
-        *:yes:*)  echo "Failures testing the package";;
-    esac
-    # Show summaries of failures (suppress lines ending with '[failed in baseline]')
-    for f in $(pwd)/.tox/sagepython-sagewheels-nopypi-norequirements*/log/*-command*.log; do
-        if [ -r "$f" ]; then
-            echo "$f"
-            grep '^sage -t.*#[^]]*$' "$f"
-        fi
-    done
-    exit $status
-fi
diff --git a/build/pkgs/sagemath_repl/spkg-check b/build/pkgs/sagemath_repl/spkg-check
new file mode 120000
index 00000000000..91c6b1835fc
--- /dev/null
+++ b/build/pkgs/sagemath_repl/spkg-check
@@ -0,0 +1 @@
+../sagemath_objects/spkg-check
\ No newline at end of file