diff --git a/Makefile b/Makefile
index 004a6750920..414398ddf0d 100644
--- a/Makefile
+++ b/Makefile
@@ -101,7 +101,7 @@ pypi-wheels:
 	    rm -f venv/var/lib/sage/installed/$$a-*; \
 	done
 	for a in $(PYPI_WHEEL_PACKAGES); do \
-	    $(MAKE) SAGE_EDITABLE=no $$a; \
+	    $(MAKE) SAGE_EDITABLE=no SAGE_WHEELS=yes $$a; \
 	done
 	@echo "Built wheels are in venv/var/lib/sage/wheels/"
 
@@ -112,7 +112,7 @@ wheels:
 	    rm -f venv/var/lib/sage/installed/$$a-*; \
 	done
 	for a in $(WHEEL_PACKAGES); do \
-	    $(MAKE) SAGE_EDITABLE=no $$a; \
+	    $(MAKE) SAGE_EDITABLE=no SAGE_WHEELS=yes $$a; \
 	done
 	@echo "Built wheels are in venv/var/lib/sage/wheels/"
 
diff --git a/build/bin/sage-build-env b/build/bin/sage-build-env
index ed999b703f0..87cd0fde5f3 100644
--- a/build/bin/sage-build-env
+++ b/build/bin/sage-build-env
@@ -31,6 +31,10 @@ if [ "x$SAGE_BUILD_ENV_SOURCED" = "x" ]; then
     if [ "x$SAGE_EDITABLE" = "x" ]; then
         export SAGE_EDITABLE="$CONFIGURED_SAGE_EDITABLE"
     fi
+    # Likewise for SAGE_WHEELS
+    if [ "x$SAGE_WHEELS" = "x" ]; then
+        export SAGE_WHEELS="$CONFIGURED_SAGE_WHEELS"
+    fi
 
     # This is usually blank if the system GMP is used, or $SAGE_LOCAL otherwise
     if [ -n "$SAGE_GMP_PREFIX" ]; then
diff --git a/build/bin/sage-build-env-config.in b/build/bin/sage-build-env-config.in
index 58d6bd5e5d7..b00fd2a3f99 100644
--- a/build/bin/sage-build-env-config.in
+++ b/build/bin/sage-build-env-config.in
@@ -58,3 +58,4 @@ export SAGE_SUITESPARSE_PREFIX="@SAGE_SUITESPARSE_PREFIX@"
 export SAGE_CONFIGURE_FFLAS_FFPACK="@SAGE_CONFIGURE_FFLAS_FFPACK@"
 
 export CONFIGURED_SAGE_EDITABLE="@SAGE_EDITABLE@"
+export CONFIGURED_SAGE_WHEELS="@SAGE_WHEELS@"
diff --git a/build/pkgs/sagelib/spkg-install b/build/pkgs/sagelib/spkg-install
index 473cfe06db8..8e5e97f2688 100755
--- a/build/pkgs/sagelib/spkg-install
+++ b/build/pkgs/sagelib/spkg-install
@@ -60,17 +60,30 @@ if [ "$SAGE_EDITABLE" = yes ]; then
     # under the old distribution name "sage" (before #30912, which switched to setuptools
     # and renamed the distribution to "sagemath-standard").  There is no clean way to uninstall
     # them, so we just use rm.
-    (cd "$SITEPACKAGESDIR" && rm -rf sage sage_setup sage-[1-9]*.egg-info sage-[1-9]*.dist-info)
+    (cd "$SITEPACKAGESDIR" && rm -rf sage sage-[1-9]*.egg-info sage-[1-9]*.dist-info)
     time sdh_pip_editable_install .
+
+    if [ "$SAGE_WHEELS" = yes ]; then
+        # Additionally build a wheel (for use in other venvs)
+        cd $SAGE_PKGS/sagelib/src && time sdh_setup_bdist_wheel && sdh_store_wheel .
+    fi
 else
     # Make sure that an installed old version of sagelib in which sage is an ordinary package
     # does not shadow the namespace package sage during the build.
     (cd "$SITEPACKAGESDIR" && rm -f sage/__init__.py)
     # Likewise, we should remove the egg-link that may have been installed previously.
     (cd "$SITEPACKAGESDIR" && rm -f sagemath-standard.egg-link)
-    # Use --no-build-isolation to avoid rebuilds because of dependencies:
-    # Compiling sage/interfaces/sagespawn.pyx because it depends on /private/var/folders/38/wnh4gf1552g_crsjnv2vmmww0000gp/T/pip-build-env-609n5985/overlay/lib/python3.10/site-packages/Cython/Includes/posix/unistd.pxd
-    time sdh_pip_install --no-build-isolation .
+
+    if [ "$SAGE_WHEELS" = yes ]; then
+        # Use --no-build-isolation to avoid rebuilds because of dependencies:
+        # Compiling sage/interfaces/sagespawn.pyx because it depends on /private/var/folders/38/wnh4gf1552g_crsjnv2vmmww0000gp/T/pip-build-env-609n5985/overlay/lib/python3.10/site-packages/Cython/Includes/posix/unistd.pxd
+        time sdh_pip_install --no-build-isolation .
+    else
+        # We no longer use the install-cleaner for installation directory cleaning.
+        # So uninstall first.
+        time sdh_pip_uninstall sagemath-standard
+        time python3 -u setup.py --no-user-cfg build install || exit 1
+    fi
 fi
 
 # Trac #33103: The temp.* directories are large after a full build.
diff --git a/configure.ac b/configure.ac
index 10351b8c416..ca5003e83e0 100644
--- a/configure.ac
+++ b/configure.ac
@@ -132,6 +132,12 @@ AC_ARG_ENABLE([editable],
               [AC_SUBST([SAGE_EDITABLE], [$enableval])],
               [AC_SUBST([SAGE_EDITABLE], [yes])])
 
+AC_ARG_ENABLE([wheels],
+              [AS_HELP_STRING([--enable-wheels],
+                              [build and update wheels for the Sage library])],
+              [AC_SUBST([SAGE_WHEELS], [$enableval])],
+              [])
+
 # Check whether we are on a supported platform
 AC_CANONICAL_BUILD()
 AC_CANONICAL_HOST()