diff --git a/debian.master/control.stub.in b/debian.master/control.stub.in
index 8efedc6eb19a..b1b082edf4ee 100644
--- a/debian.master/control.stub.in
+++ b/debian.master/control.stub.in
@@ -37,7 +37,7 @@ Build-Depends:
  libnuma-dev [amd64 arm64 ppc64el s390x] <!stage1>,
  dkms <!stage1>,
  curl <!stage1>,
- zstd [amd64 s390x] <!stage1>,
+ zstd <!stage1>,
  pahole [amd64 arm64 armhf ppc64el s390x riscv64] | dwarves (>= 1.21) [amd64 arm64 armhf ppc64el s390x riscv64] <!stage1>,
  rustc [amd64],
  rust-src [amd64],
diff --git a/debian/rules.d/2-binary-arch.mk b/debian/rules.d/2-binary-arch.mk
index b90e26df1e8d..182ad2afa554 100644
--- a/debian/rules.d/2-binary-arch.mk
+++ b/debian/rules.d/2-binary-arch.mk
@@ -576,6 +576,8 @@ define dh_all
 	dh_installchangelogs -p$(1)
 	dh_installdocs -p$(1)
 	dh_compress -p$(1)
+	# Compress kernel modules
+	find debian/$(1) -name '*.ko' -print0 | xargs -0 -n1 -P $(CONCURRENCY_LEVEL) zstd -19 --quiet --rm
 	dh_fixperms -p$(1) -X/boot/
 	dh_shlibdeps -p$(1) $(shlibdeps_opts)
 	dh_installdeb -p$(1)
@@ -628,7 +630,7 @@ binary-%: checks-%
 	dh_testroot
 
 	$(call dh_all,$(pkgimg)) -- -Znone
-	$(call dh_all,$(pkgimg_mods))
+	$(call dh_all,$(pkgimg_mods)) -- -Znone
 
 ifeq ($(do_extras_package),true)
   ifeq ($(ship_extras_package),false)
@@ -640,13 +642,13 @@ ifeq ($(do_extras_package),true)
 		| tee -a $(target_flavour).not-shipped.log;
   else
 	if [ -f $(DEBIAN)/control.d/$(target_flavour).inclusion-list ] ; then \
-		$(call dh_all_inline,$(pkgimg_ex)); \
+		$(call dh_all_inline,$(pkgimg_ex)) -- -Znone; \
 	fi
   endif
 endif
 
 	$(foreach _m,$(all_standalone_dkms_modules), \
-	  $(if $(enable_$(_m)),$(call dh_all,$(dkms_$(_m)_pkg_name)-$*);)\
+	  $(if $(enable_$(_m)),$(call dh_all,$(dkms_$(_m)_pkg_name)-$*) -- -Znone;)\
 	)
 
 	$(call dh_all,$(pkgbldinfo))