diff --git a/Jenkinsfile b/Jenkinsfile
index a4830ee131..45daa90e12 100644
--- a/Jenkinsfile
+++ b/Jenkinsfile
@@ -29,7 +29,7 @@ test_steps = [
 				sh("git -C cli checkout $branch")
 				sh('git clone https://github.com/docker/engine.git')
 				sh("git -C engine checkout $branch")
-				sh('make VERSION=0.0.1-dev DOCKER_BUILD_PKGS=ubuntu-xenial ENGINE_DIR=$(pwd)/engine CLI_DIR=$(pwd)/cli deb')
+				sh('make -C deb VERSION=0.0.1-dev ENGINE_DIR=$(pwd)/engine CLI_DIR=$(pwd)/cli ubuntu-xenial')
 			}
 		}
 	},
@@ -41,7 +41,7 @@ test_steps = [
 				sh("git -C cli checkout $branch")
 				sh('git clone https://github.com/docker/engine.git')
 				sh("git -C engine checkout $branch")
-				sh('make VERSION=0.0.1-dev DOCKER_BUILD_PKGS=centos-7 ENGINE_DIR=$(pwd)/engine CLI_DIR=$(pwd)/cli rpm')
+				sh('make -C rpm VERSION=0.0.1-dev ENGINE_DIR=$(pwd)/engine CLI_DIR=$(pwd)/cli centos-7')
 			}
 		}
 	},
diff --git a/Makefile b/Makefile
index 5147089232..bf786929da 100644
--- a/Makefile
+++ b/Makefile
@@ -36,18 +36,12 @@ clean: clean-image ## remove build artifacts
 	$(MAKE) -C static clean
 
 .PHONY: rpm
-rpm: DOCKER_BUILD_PKGS:=$(shell find rpm -type d | grep ".*-.*" | sed 's/^rpm\///')
 rpm: ## build rpm packages
-	for p in $(DOCKER_BUILD_PKGS); do \
-		$(MAKE) -C $@ VERSION=$(VERSION) ENGINE_DIR=$(ENGINE_DIR) CLI_DIR=$(CLI_DIR) GO_VERSION=$(GO_VERSION) $${p}; \
-	done
+	$(MAKE) -C $@ VERSION=$(VERSION) ENGINE_DIR=$(ENGINE_DIR) CLI_DIR=$(CLI_DIR) GO_VERSION=$(GO_VERSION) rpm
 
 .PHONY: deb
-deb: DOCKER_BUILD_PKGS:=$(shell find deb -type d | grep ".*-.*" | sed 's/^deb\///')
 deb: ## build deb packages
-	for p in $(DOCKER_BUILD_PKGS); do \
-		$(MAKE) -C $@ VERSION=$(VERSION) ENGINE_DIR=$(ENGINE_DIR) CLI_DIR=$(CLI_DIR) GO_VERSION=$(GO_VERSION) $${p}; \
-	done
+	$(MAKE) -C $@ VERSION=$(VERSION) ENGINE_DIR=$(ENGINE_DIR) CLI_DIR=$(CLI_DIR) GO_VERSION=$(GO_VERSION) deb
 
 .PHONY: static
 static: DOCKER_BUILD_PKGS:=static-linux cross-mac cross-win cross-arm
diff --git a/deb/Makefile b/deb/Makefile
index 55391eceab..2a6f5b3572 100644
--- a/deb/Makefile
+++ b/deb/Makefile
@@ -38,6 +38,11 @@ RUN=docker run --rm -i \
 SOURCE_FILES=engine-image cli.tgz engine.tgz docker.service docker.socket distribution_based_engine.json plugin-installers.tgz
 SOURCES=$(addprefix sources/, $(SOURCE_FILES))
 
+DEBIAN_VERSIONS := debian-stretch debian-buster
+UBUNTU_VERSIONS := ubuntu-xenial ubuntu-bionic ubuntu-cosmic ubuntu-disco
+RASPBIAN_VERSIONS := raspbian-stretch raspbian-buster
+DISTROS := $(DEBIAN_VERSIONS) $(UBUNTU_VERSIONS) $(RASPBIAN_VERSIONS)
+
 .PHONY: help
 help: ## show make targets
 	@awk 'BEGIN {FS = ":.*?## "} /^[a-zA-Z_-]+:.*?## / {sub("\\\\n",sprintf("\n%22c"," "), $$2);printf " \033[36m%-20s\033[0m  %s\n", $$1, $$2}' $(MAKEFILE_LIST)
@@ -55,34 +60,20 @@ engine-$(ARCH).tar:
 	docker save -o $@ $$(cat ../image/image-linux)
 
 .PHONY: deb
-deb: ubuntu debian raspbian ## build all deb packages
+deb: ubuntu debian ## build all deb packages except for raspbian
 
 .PHONY: ubuntu
-ubuntu: ubuntu-bionic ubuntu-xenial ## build all ubuntu deb packages
+ubuntu: $(UBUNTU_VERSIONS) ## build all ubuntu deb packages
 
 .PHONY: debian
-debian: debian-stretch debian-buster ## build all debian deb packages
+debian: $(DEBIAN_VERSIONS) ## build all debian deb packages
 
 .PHONY: raspbian
-raspbian: raspbian-stretch raspbian-buster ## build all raspbian deb packages
-
-.PHONY: ubuntu-%
-## build ubuntu deb packages
-ubuntu-%: $(SOURCES)
-	$(BUILD)
-	$(RUN)
-	$(CHOWN) -R $(shell id -u):$(shell id -g) debbuild/$@
-
-.PHONY: debian-%
-## build debian deb packages
-debian-%: $(SOURCES)
-	$(BUILD)
-	$(RUN)
-	$(CHOWN) -R $(shell id -u):$(shell id -g) debbuild/$@
+raspbian: $(RASPBIAN_VERSIONS) ## build all raspbian deb packages
 
-.PHONY: raspbian-%
-## build raspbian deb packages
-raspbian-%: $(SOURCES)
+.PHONY: $(DISTROS)
+$(DISTROS): $(SOURCES)
+	@echo "== Building packages for $@ =="
 	$(BUILD)
 	$(RUN)
 	$(CHOWN) -R $(shell id -u):$(shell id -g) debbuild/$@
diff --git a/rpm/Makefile b/rpm/Makefile
index d861f92445..710919edad 100644
--- a/rpm/Makefile
+++ b/rpm/Makefile
@@ -42,6 +42,9 @@ RUN?=$(RPMBUILD) rpmbuild-$@/$(ARCH) $(RPMBUILD_FLAGS)
 SOURCE_FILES=engine-image engine.tgz cli.tgz docker.service docker.socket distribution_based_engine.json plugin-installers.tgz
 SOURCES=$(addprefix rpmbuild/SOURCES/, $(SOURCE_FILES))
 
+FEDORA_RELEASES := fedora-31 fedora-30 fedora-29 fedora-28
+CENTOS_RELEASES := centos-7
+
 .PHONY: help
 help: ## show make targets
 	@awk 'BEGIN {FS = ":.*?## "} /^[a-zA-Z_-]+:.*?## / {sub("\\\\n",sprintf("\n%22c"," "), $$2);printf " \033[36m%-20s\033[0m  %s\n", $$1, $$2}' $(MAKEFILE_LIST)
@@ -61,22 +64,14 @@ clean: ## remove build artifacts
 rpm: fedora centos ## build all rpm packages
 
 .PHONY: fedora
-fedora: fedora-31 fedora-30 fedora-29 fedora-28 ## build all fedora rpm packages
+fedora: $(FEDORA_RELEASES) ## build all fedora rpm packages
 
 .PHONY: centos
-centos: centos-7 ## build all centos rpm packages
-
-.PHONY: fedora-%
-fedora-%: ## build fedora rpm packages
-fedora-%: $(SOURCES)
-	$(CHOWN) -R root:root rpmbuild
-	$(BUILD)
-	$(RUN)
-	$(CHOWN) -R $(shell id -u):$(shell id -g) rpmbuild
+centos: $(CENTOS_RELEASES) ## build all centos rpm packages
 
-.PHONY: centos-7
-centos-7: ## build centos-7 rpm packages
-centos-7: $(SOURCES)
+.PHONY: $(FEDORA_RELEASES) $(CENTOS_RELEASES)
+$(FEDORA_RELEASES) $(CENTOS_RELEASES): $(SOURCES)
+	@echo "== Building packages for $@ =="
 	$(CHOWN) -R root:root rpmbuild
 	$(BUILD)
 	$(RUN)