diff --git a/azure/backend.go b/azure/backend.go
index cd3a4654..25ff9809 100644
--- a/azure/backend.go
+++ b/azure/backend.go
@@ -42,7 +42,10 @@ import (
 	"github.com/docker/api/errdefs"
 )
 
-const singleContainerName = "single--container--aci"
+const (
+	singleContainerName       = "single--container--aci"
+	composeContainerSeparator = "_"
+)
 
 // ErrNoSuchContainer is returned when the mentioned container does not exist
 var ErrNoSuchContainer = errors.New("no such container")
@@ -135,7 +138,7 @@ func (cs *aciContainerService) List(ctx context.Context, _ bool) ([]containers.C
 			if *container.Name == singleContainerName {
 				containerID = *containerGroup.Name
 			} else {
-				containerID = *containerGroup.Name + "_" + *container.Name
+				containerID = *containerGroup.Name + composeContainerSeparator + *container.Name
 			}
 			status := "Unknown"
 			if container.InstanceView != nil && container.InstanceView.CurrentState != nil {
@@ -155,6 +158,10 @@ func (cs *aciContainerService) List(ctx context.Context, _ bool) ([]containers.C
 }
 
 func (cs *aciContainerService) Run(ctx context.Context, r containers.ContainerConfig) error {
+	if strings.Contains(r.ID, composeContainerSeparator) {
+		return errors.New(fmt.Sprintf("invalid container name. ACI container name cannot include %q", composeContainerSeparator))
+	}
+
 	var ports []types.ServicePortConfig
 	for _, p := range r.Ports {
 		ports = append(ports, types.ServicePortConfig{
@@ -204,7 +211,7 @@ func (cs *aciContainerService) Stop(ctx context.Context, containerName string, t
 }
 
 func getGroupAndContainerName(containerID string) (groupName string, containerName string) {
-	tokens := strings.Split(containerID, "_")
+	tokens := strings.Split(containerID, composeContainerSeparator)
 	groupName = tokens[0]
 	if len(tokens) > 1 {
 		containerName = tokens[len(tokens)-1]
@@ -258,7 +265,11 @@ func (cs *aciContainerService) Logs(ctx context.Context, containerName string, r
 }
 
 func (cs *aciContainerService) Delete(ctx context.Context, containerID string, _ bool) error {
-	cg, err := deleteACIContainerGroup(ctx, cs.ctx, containerID)
+	groupName, containerName := getGroupAndContainerName(containerID)
+	if groupName != containerID {
+		return errors.New(fmt.Sprintf("cannot delete service %q from compose app %q, you must delete the entire compose app with docker compose down", containerName, groupName))
+	}
+	cg, err := deleteACIContainerGroup(ctx, cs.ctx, groupName)
 	if err != nil {
 		return err
 	}
@@ -315,9 +326,16 @@ func (cs *aciComposeService) Up(ctx context.Context, opts cli.ProjectOptions) er
 }
 
 func (cs *aciComposeService) Down(ctx context.Context, opts cli.ProjectOptions) error {
-	project, err := cli.ProjectFromOptions(&opts)
-	if err != nil {
-		return err
+	var project types.Project
+
+	if opts.Name != "" {
+		project = types.Project{Name: opts.Name}
+	} else {
+		fullProject, err := cli.ProjectFromOptions(&opts)
+		if err != nil {
+			return err
+		}
+		project = *fullProject
 	}
 	logrus.Debugf("Down on project with name %q\n", project.Name)
 
diff --git a/azure/backend_test.go b/azure/backend_test.go
index 6f50678d..c7090489 100644
--- a/azure/backend_test.go
+++ b/azure/backend_test.go
@@ -17,8 +17,11 @@
 package azure
 
 import (
+	"context"
 	"testing"
 
+	"github.com/docker/api/containers"
+
 	"github.com/stretchr/testify/suite"
 
 	. "github.com/onsi/gomega"
@@ -42,6 +45,22 @@ func (suite *BackendSuiteTest) TestGetContainerName() {
 	Expect(container).To(Equal("service1"))
 }
 
+func (suite *BackendSuiteTest) TestErrorMessageDeletingContainerFromComposeApplication() {
+	service := aciContainerService{}
+	err := service.Delete(context.TODO(), "compose-app_service1", false)
+
+	Expect(err).NotTo(BeNil())
+	Expect(err.Error()).To(Equal("cannot delete service \"service1\" from compose app \"compose-app\", you must delete the entire compose app with docker compose down"))
+}
+
+func (suite *BackendSuiteTest) TestErrorMessageRunSingleContainerNameWithComposeSeparator() {
+	service := aciContainerService{}
+	err := service.Run(context.TODO(), containers.ContainerConfig{ID: "container_name"})
+
+	Expect(err).NotTo(BeNil())
+	Expect(err.Error()).To(Equal("invalid container name. ACI container name cannot include \"_\""))
+}
+
 func TestBackendSuite(t *testing.T) {
 	RegisterTestingT(t)
 	suite.Run(t, new(BackendSuiteTest))
diff --git a/example/backend.go b/example/backend.go
index 076b4087..c5da8bf1 100644
--- a/example/backend.go
+++ b/example/backend.go
@@ -22,9 +22,10 @@ import (
 	"context"
 	"errors"
 	"fmt"
-	"github.com/compose-spec/compose-go/cli"
 	"io"
 
+	"github.com/compose-spec/compose-go/cli"
+
 	"github.com/docker/api/context/cloud"
 
 	"github.com/docker/api/backend"
diff --git a/tests/aci-e2e/e2e-aci_test.go b/tests/aci-e2e/e2e-aci_test.go
index e09ff74c..41687fbb 100644
--- a/tests/aci-e2e/e2e-aci_test.go
+++ b/tests/aci-e2e/e2e-aci_test.go
@@ -297,7 +297,7 @@ func (s *E2eACISuite) TestACIBackend() {
 	})
 
 	s.T().Run("shutdown compose app", func(t *testing.T) {
-		s.NewDockerCommand("compose", "down", "-f", composeFile, "--project-name", "acidemo").ExecOrDie()
+		s.NewDockerCommand("compose", "down", "--project-name", "acidemo").ExecOrDie()
 	})
 
 	s.T().Run("switches back to default context", func(t *testing.T) {