diff --git a/build/bin/sage-site b/build/bin/sage-site
index 413abff4dd1..0472f5652b3 100755
--- a/build/bin/sage-site
+++ b/build/bin/sage-site
@@ -170,7 +170,7 @@ if [ "$1" = '-i' ]; then
     # First, uninstall the packages if -f was given
     if [ "$FORCE_INSTALL" = yes ]; then
         for PKG in $PACKAGES; do
-            $MAKE "$PKG-clean" || true  # Ignore errors
+            $MAKE "$PKG-uninstall" || true  # Ignore errors
         done
     fi
 
diff --git a/build/make/Makefile.in b/build/make/Makefile.in
index d8ea784cf02..f7cd947b97e 100644
--- a/build/make/Makefile.in
+++ b/build/make/Makefile.in
@@ -114,7 +114,7 @@ INSTALLED_PACKAGE_INSTS = \
 # All previously installed standard/optional/experimental packages that are to be uninstalled
 OPTIONAL_UNINSTALLED_PACKAGES = @SAGE_OPTIONAL_UNINSTALLED_PACKAGES@
 UNINSTALLED_PACKAGES = $(OPTIONAL_UNINSTALLED_PACKAGES)
-UNINSTALLED_PACKAGES_CLEANS = $(UNINSTALLED_PACKAGES:%=%-clean)
+UNINSTALLED_PACKAGES_UNINSTALLS = $(UNINSTALLED_PACKAGES:%=%-uninstall)
 
 # All packages which should be downloaded
 SDIST_PACKAGES = @SAGE_SDIST_PACKAGES@
@@ -167,7 +167,7 @@ $(foreach tree,SAGE_LOCAL SAGE_VENV SAGE_DOCS, \
                $(foreach pkgname,$(INSTALLED_PACKAGES), \
                          $(if $(findstring $(tree),$(trees_$(pkgname))), \
                               $(inst_$(pkgname))))) \
-    $(eval $(tree)_CLEANED_PACKAGE_CLEANS = \
+    $(eval $(tree)_UNINSTALLED_PACKAGE_UNINSTALLS = \
                $(foreach pkgname,$(INSTALLED_PACKAGES), \
                          $(if $(findstring $(tree),$(trees_$(pkgname))), \
                               $(inst_$(pkgname))))))
@@ -190,8 +190,8 @@ else
 PLUS =
 endif
 
-# List of targets that can be run using `sage -i` or `sage -f`
-# These should generally have an associated -clean target for `sage -f` to
+# List of targets that can be run (in addition to names of packages) using `sage -i` or `sage -f`
+# These should generally have an associated -uninstall target for `sage -f` to
 # work correctly
 SAGE_I_TARGETS = sagelib doc
 
@@ -242,24 +242,24 @@ base-toolchain: _clean-broken-gcc base
 
 # All targets except for the base packages and except the documentation
 all-sage: \
-		$(SAGE_LOCAL_INSTALLED_PACKAGE_INSTS) $(SAGE_LOCAL_UNINSTALLED_PACKAGES_CLEANS) \
-		$(SAGE_VENV_INSTALLED_PACKAGE_INSTS)  $(SAGE_VENV_UNINSTALLED_PACKAGES_CLEANS)
+		$(SAGE_LOCAL_INSTALLED_PACKAGE_INSTS) $(SAGE_LOCAL_UNINSTALLED_PACKAGES_UNINSTALLS) \
+		$(SAGE_VENV_INSTALLED_PACKAGE_INSTS)  $(SAGE_VENV_UNINSTALLED_PACKAGES_UNINSTALLS)
 
 # Same but filtered by installation trees:
 all-build-local: toolchain-deps
 	+$(MAKE_REC) all-sage-local
 
-all-sage-local: $(SAGE_LOCAL_INSTALLED_PACKAGE_INSTS) $(SAGE_LOCAL_UNINSTALLED_PACKAGES_CLEANS)
+all-sage-local: $(SAGE_LOCAL_INSTALLED_PACKAGE_INSTS) $(SAGE_LOCAL_UNINSTALLED_PACKAGES_UNINSTALLS)
 
 all-build-venv: toolchain-deps
 	+$(MAKE_REC) all-sage-venv
 
-all-sage-venv:  $(SAGE_VENV_INSTALLED_PACKAGE_INSTS)  $(SAGE_VENV_UNINSTALLED_PACKAGES_CLEANS)
+all-sage-venv:  $(SAGE_VENV_INSTALLED_PACKAGE_INSTS)  $(SAGE_VENV_UNINSTALLED_PACKAGES_UNINSTALLS)
 
 all-build-docs: toolchain-deps
 	+$(MAKE_REC) all-sage-docs
 
-all-sage-docs:  $(SAGE_DOCS_INSTALLED_PACKAGE_INSTS) $(SAGE_DOCS_UNINSTALLED_PACKAGES_CLEANS)
+all-sage-docs:  $(SAGE_DOCS_INSTALLED_PACKAGE_INSTS) $(SAGE_DOCS_UNINSTALLED_PACKAGES_UNINSTALLS)
 
 # Download all packages which should be inside an sdist tarball (the -B
 # option to make forces all targets to be built unconditionally)
@@ -370,6 +370,27 @@ _clean-broken-gcc:
 	   rm -f "$(SAGE_ROOT)/build/make/.clean-broken-gcc"; \
 	   echo "Cleaned up old broken GCC install"; \
 	fi
+
+# Implicit rules for uninstalling packages that no longer exist in the source tree.
+%-SAGE_LOCAL-uninstall:
+	@package=$@; \
+	package=$${package%%-*}; \
+	if [ -d '$(SAGE_LOCAL)' ]; then \
+	    sage-spkg-uninstall $$package; \
+	fi
+
+%-SAGE_VENV-uninstall:
+	@package=$@; \
+	package=$${package%%-*}; \
+	if [ -d '$(SAGE_VENV)' ]; then \
+	    sage-spkg-uninstall $$package $(SAGE_VENV); \
+	fi
+
+%-uninstall:
+	@package=$@; \
+	package=$${package%%-*}; \
+	$(MAKE) $$package-SAGE_LOCAL-uninstall $$package-SAGE_VENV-uninstall
+
 #==============================================================================
 # Setting SAGE_CHECK... variables
 #==============================================================================
@@ -455,7 +476,7 @@ pkg_deps = \
 # <pkgname>-no-deps:
 #     +$(AM_V_at)sage-logger -p '$(SAGE_SPKG) <pkgname>-<pkgvers>' '$(SAGE_LOGS)/<pkgname>-<pkgvers>.log'
 #
-# <pkgname>-clean:
+# <pkgname>-uninstall:
 #     sage-spkg-uninstall <pkgname> '$(SAGE_LOCAL)'
 #
 # So <pkgname>-build-deps installs just the dependencies, while
@@ -470,7 +491,7 @@ pkg_deps = \
 #
 # python3: $(INST)/python3-3.7.3
 #
-# python3-clean:
+# python3-uninstall:
 #     sage-spkg-uninstall python3 '$(SAGE_LOCAL)'
 #
 # Note: In these rules the $(INST)/<pkgname>-<pkgvers> target is used
@@ -512,15 +533,17 @@ $(1)-$(4)-no-deps:
 
 $(1)-no-deps: $(1)-$(4)-no-deps
 
-$(1)-$(4)-clean:
+$(1)-$(4)-uninstall:
 	if [ -d '$$($(4))' ]; then \
 	    sage-spkg-uninstall $(if $(filter $(1),$(TOOLCHAIN_DEPS)),--keep-files) \
 		$(1) '$$($(4))'; \
 	fi
 
-$(1)-clean: $(1)-$(4)-clean
+$(1)-uninstall: $(1)-$(4)-uninstall
+
+$(1)-clean: $(1)-uninstall
 
-.PHONY: $(1) $(1)-clean $(1)-build-deps $(1)-no-deps
+.PHONY: $(1) $(1)-$(4)-uninstall $(1)-uninstall $(1)-clean $(1)-build-deps $(1)-no-deps
 endef #################################################################
 
 $(foreach pkgname, $(NORMAL_PACKAGES),\
@@ -543,7 +566,7 @@ endif
 # <pkgname>: <dependencies>
 #     $(AM_V_at)sage-logger -p 'sage --pip install ...' '$(SAGE_LOGS)/<pkgname>.log'
 #
-# <pkgname>-clean:
+# <pkgname>-uninstall:
 #     -sage --pip uninstall -y ...
 
 # Positional arguments:
@@ -558,10 +581,12 @@ $(1): $(2)
 $(1)-no-deps:
 	$(AM_V_at)sage-logger -p 'sage --pip install -r "$$(SAGE_ROOT)/build/pkgs/$(1)/requirements.txt"' '$$(SAGE_LOGS)/$(1).log'
 
-$(1)-clean:
+$(1)-uninstall:
 	-sage --pip uninstall --isolated --yes --no-input -r '$$(SAGE_ROOT)/build/pkgs/$(1)/requirements.txt'
 
-.PHONY: $(1) $(1)-clean $(1)-build-deps $(1)-no-deps
+$(1)-clean: $(1)-uninstall
+
+.PHONY: $(1) $(1)-uninstall $(1)-clean $(1)-build-deps $(1)-no-deps
 endef
 
 $(foreach pkgname,$(PIP_PACKAGES),\
@@ -587,7 +612,7 @@ endif
 #
 # <pkgname>: $(INST)/<pkgname>-<pkgvers>
 #
-# <pkgname>-clean:
+# <pkgname>-uninstall:
 #     -$(AM_V_at)cd '$SAGE_ROOT' && \\
 #         . '$SAGE_ROOT/src/bin/sage-env-config' && \\
 #         . '$SAGE_ROOT/src/bin/sage-env' && \\
@@ -664,7 +689,7 @@ $(1)-tox-%: FORCE
 		SAGE_SPKG_WHEELS=$$(SAGE_LOCAL)/var/lib/sage/wheels \
 		tox -v -v -v -e $$*
 
-.PHONY: $(1) $(1)-uninstall $(1)-build-deps $(1)-no-deps $(1)-clean
+.PHONY: $(1) $(1)-uninstall $(1)-clean $(1)-build-deps $(1)-no-deps $(1)-clean
 
 endef
 
diff --git a/build/sage_bootstrap/uninstall.py b/build/sage_bootstrap/uninstall.py
index bfd5aae9a80..1ce039921fc 100644
--- a/build/sage_bootstrap/uninstall.py
+++ b/build/sage_bootstrap/uninstall.py
@@ -1,5 +1,5 @@
 """
-Command-line script for uninstalling an existing Sage spkg from $SAGE_LOCAL.
+Command-line script for uninstalling an existing SPKG from an installation tree ($SAGE_LOCAL, $SAGE_VENV).
 
 This performs two types of uninstallation:
 
@@ -14,9 +14,10 @@
 
     2) New-style uninstallation: More recently installed packages that were
        installed with staged installation have a record of all files installed
-       by that package.  That file is stored in the $SAGE_SPKG_INST directory
-       (typically $SAGE_LOCAL/var/lib/sage/installed) and is created when the
-       spkg is installed.  This is a JSON file containing some meta-data about
+       by that package.  That file is stored in the directory
+       $SAGE_LOCAL/var/lib/sage/installed or $SAGE_VENV/var/lib/sage/installed
+       and is created when the spkg is installed.
+       This is a JSON file containing some meta-data about
        the package, including the list of all files associated with the
        package.  This script removes all these files, including the record
        file.  Any directories that are empty after files are removed from them
@@ -50,14 +51,13 @@
 
 def uninstall(spkg_name, sage_local, keep_files=False, verbose=False):
     """
-    Given a package name and path to SAGE_LOCAL, uninstall that package from
-    SAGE_LOCAL if it is currently installed.
+    Given a package name and path to an installation tree (SAGE_LOCAL or SAGE_VENV),
+    uninstall that package from that tree if it is currently installed.
     """
 
-    # The default path to this directory; however its value should be read
-    # from the environment if possible
+    # The path to the installation records.
+    # See SPKG_INST_RELDIR in SAGE_ROOT/build/make/Makefile.in
     spkg_inst = pth.join(sage_local, 'var', 'lib', 'sage', 'installed')
-    spkg_inst = os.environ.get('SAGE_SPKG_INST', spkg_inst)
 
     # Find all stamp files for the package; there should be only one, but if
     # there is somehow more than one we'll work with the most recent and delete
@@ -131,8 +131,9 @@ def legacy_uninstall(spkg_name, verbose=False):
 
 def modern_uninstall(spkg_name, sage_local, files, verbose=False):
     """
-    Remove all listed files from the given SAGE_LOCAL (all file paths should
-    be assumed relative to SAGE_LOCAL).
+    Remove all listed files from the given installation tree (SAGE_LOCAL or SAGE_VENV).
+
+    All file paths should be assumed relative to the installation tree.
 
     This is otherwise (currently) agnostic about what package is actually
     being uninstalled--all it cares about is removing a list of files.
@@ -259,20 +260,6 @@ def dir_type(path):
     return path
 
 
-def spkg_type(pkg):
-    """
-    A custom argument 'type' for spkgs--checks whether the given package name
-    is a known spkg.
-    """
-    pkgbase = pth.join(PKGS, pkg)
-
-    if not pth.isdir(pkgbase):
-        raise argparse.ArgumentTypeError(
-            "'{0}' is not a known spkg".format(pkg))
-
-    return pkg
-
-
 def make_parser():
     """Returns the command-line argument parser for sage-spkg-uninstall."""
 
@@ -283,10 +270,10 @@ def make_parser():
         epilog='\n'.join(doc_lines[1:]).strip(),
         formatter_class=argparse.RawDescriptionHelpFormatter)
 
-    parser.add_argument('spkg', type=spkg_type, help='the spkg to uninstall')
+    parser.add_argument('spkg', type=str, help='the spkg to uninstall')
     parser.add_argument('sage_local', type=dir_type, nargs='?',
                         default=os.environ.get('SAGE_LOCAL'),
-                        help='the SAGE_LOCAL path (default: the $SAGE_LOCAL '
+                        help='the path of the installation tree (default: the $SAGE_LOCAL '
                              'environment variable if set)')
     parser.add_argument('-v', '--verbose', action='store_true',
                         help='verbose output showing all files removed')
@@ -305,7 +292,7 @@ def run(argv=None):
     args = parser.parse_args(argv if argv is not None else sys.argv[1:])
 
     if args.sage_local is None:
-        print('Error: SAGE_LOCAL must be specified either at the command '
+        print('Error: An installation tree must be specified either at the command '
               'line or in the $SAGE_LOCAL environment variable',
               file=sys.stderr)
         sys.exit(1)
diff --git a/tox.ini b/tox.ini
index ff0f1b690b4..9ebf02a828d 100644
--- a/tox.ini
+++ b/tox.ini
@@ -90,7 +90,7 @@ envlist =
     #
     # Or to rebuild a package with verbose output:
     #
-    #   $ tox -e local-homebrew-macos-standard -- ppl-clean ppl V=1
+    #   $ tox -e local-homebrew-macos-standard -- ppl-uninstall ppl V=1
     #
     # The variant "local-homebrew-macos-usrlocal" uses the global installation in /usr/local
     # instead.  It may install packages or update packages.  It will not remove packages.