diff --git a/Makefile b/Makefile
index ae9635b..fe90b12 100644
--- a/Makefile
+++ b/Makefile
@@ -1,6 +1,8 @@
 .PHONY: help
 
 VERSION ?= `cat VERSION`
+MAJ_VERSION := $(shell echo $(VERSION) | sed 's/\([0-9][0-9]*\)\.\([0-9][0-9]*\)\(\.[0-9][0-9]*\)*/\1/')
+MIN_VERSION := $(shell echo $(VERSION) | sed 's/\([0-9][0-9]*\)\.\([0-9][0-9]*\)\(\.[0-9][0-9]*\)*/\1.\2/')
 IMAGE_NAME ?= bitwalker/alpine-elixir-phoenix
 
 help:
@@ -10,8 +12,19 @@ help:
 test: ## Test the Docker image
 	docker run --rm -it $(IMAGE_NAME):$(VERSION) elixir --version
 
-build: ## Rebuild the Docker image
-	docker build --force-rm -t $(IMAGE_NAME):$(VERSION) -t $(IMAGE_NAME):latest - < ./Dockerfile
+shell: ## Run an Elixir shell in the image
+	docker run --rm -it $(IMAGE_NAME):$(VERSION) iex
+
+sh: ## Boot to a shell prompt
+	docker run --rm -it $(IMAGE_NAME):$(VERSION) /bin/bash
+
+build: ## Build the Docker image
+	docker build --force-rm -t $(IMAGE_NAME):$(VERSION) -t $(IMAGE_NAME):$(MIN_VERSION) -t $(IMAGE_NAME):$(MAJ_VERSION) -t $(IMAGE_NAME):latest - < ./Dockerfile
+
+clean: ## Clean up generated images
+	@docker rmi --force $(IMAGE_NAME):$(VERSION) $(IMAGE_NAME):$(MIN_VERSION) $(IMAGE_NAME):$(MAJ_VERSION) $(IMAGE_NAME):latest
+
+rebuild: clean build ## Rebuild the Docker image
 
 release: build ## Rebuild and release the Docker image to Docker Hub
 	docker push $(IMAGE_NAME):$(VERSION)