diff --git a/debian/control b/debian/control
index c4ce0d8e9..f128ea8e0 100644
--- a/debian/control
+++ b/debian/control
@@ -6,6 +6,7 @@ Uploaders: Lisandro Damián Nicanor Pérez Meyer <lisandro@debian.org>,
            Felix Geyer <fgeyer@debian.org>,
            Timo Röhling <roehling@debian.org>
 Build-Depends: debhelper-compat (= 13),
+               cmake <cross>,
                freebsd-glue [kfreebsd-any],
                libarchive-dev (>= 3.3.3) <!pkg.cmake.bootstrap>,
                libcurl4-openssl-dev <!pkg.cmake.bootstrap> | libcurl-ssl-dev <!pkg.cmake.bootstrap>,
@@ -16,8 +17,8 @@ Build-Depends: debhelper-compat (= 13),
                libssl-dev <pkg.cmake.bootstrap>,
                libuv1-dev (>= 1.10) <!pkg.cmake.bootstrap>,
                procps [!hurd-any],
-               python3-sphinx,
-               python3-sphinxcontrib.qthelp | python3-sphinx (<< 2.0),
+               python3-sphinx:native,
+               python3-sphinxcontrib.qthelp:native,
                qtbase5-dev <!pkg.cmake.bootstrap !pkg.cmake.nogui>,
                zlib1g-dev <!pkg.cmake.bootstrap>
 Build-Depends-Indep:
diff --git a/debian/rules b/debian/rules
index 6882c023f..f39135f0e 100755
--- a/debian/rules
+++ b/debian/rules
@@ -42,6 +42,12 @@ BOOTSTRAP_FLAGS = --prefix=/usr --docdir=/share/doc/cmake-data --mandir=/share/m
                   --sphinx-man --sphinx-html --sphinx-flags="-D today=\"$(BUILD_DATE)\"" \
                   --init=../$(BUILD_FLAGS_FILE) --verbose
 
+CROSS_CMAKE_FLAGS = -C../$(BUILD_FLAGS_FILE) \
+                    -DCMAKE_DOC_DIR=share/doc/cmake-data \
+                    -DCMAKE_MAN_DIR=share/man \
+                    -DSPHINX_HTML=ON -DSPHINX_MAN=ON \
+                    -DSPHINX_FLAGS="-D today=\"$(BUILD_DATE)\""
+
 ifneq (,$(filter parallel=%,$(DEB_BUILD_OPTIONS)))
     NUMJOBS = $(patsubst parallel=%,%,$(filter parallel=%,$(DEB_BUILD_OPTIONS)))
     BOOTSTRAP_FLAGS += --parallel=$(NUMJOBS)
@@ -50,11 +56,17 @@ else
 endif
 ifeq (,$(filter pkg.cmake.bootstrap,$(DEB_BUILD_PROFILES)))
     BOOTSTRAP_FLAGS += --system-libs
+    CROSS_CMAKE_FLAGS += -DCMAKE_USE_SYSTEM_LIBRARIES=ON
 endif
 
 override_dh_auto_configure: $(BUILD_FLAGS_FILE)
+ifeq (,$(filter cross,$(DEB_BUILD_PROFILES)))
 	rm -rf Build && mkdir -p Build
 	cd Build && ../bootstrap $(BOOTSTRAP_FLAGS)
+else
+	dh_auto_configure --buildsystem=cmake --builddirectory=Build -- \
+		$(CROSS_CMAKE_FLAGS)
+endif
 
 ifeq ($(DEB_HOST_ARCH_OS),kfreebsd)
     # Workaround for Bug #815231: skip spuriously failing tests