diff --git a/pkg/compose/convergence.go b/pkg/compose/convergence.go
index b480b6be9d..425fc8c798 100644
--- a/pkg/compose/convergence.go
+++ b/pkg/compose/convergence.go
@@ -482,6 +482,14 @@ func (s *composeService) waitDependencies(ctx context.Context, project *types.Pr
 				case ServiceConditionRunningOrHealthy:
 					isHealthy, err := s.isServiceHealthy(ctx, waitingFor, true)
 					if err != nil {
+						// A container that exited with code 0 can be treated as
+						// successfully completed (init/oneshot containers) when the
+						// service won't be restarted by Docker after a clean exit.
+						var exitErr *containerExitError
+						if errors.As(err, &exitErr) && exitErr.exitCode == 0 && !restartsOnExit0(project, dep) {
+							s.events.On(containerEvents(waitingFor, exited)...)
+							return nil
+						}
 						if !config.Required {
 							s.events.On(containerReasonEvents(waitingFor, skippedEvent,
 								fmt.Sprintf("optional dependency %q is not running or is unhealthy", dep))...)
@@ -552,6 +560,29 @@ func (s *composeService) waitDependencies(ctx context.Context, project *types.Pr
 	return err
 }
 
+// restartsOnExit0 reports whether Docker will restart the named service after
+// it exits with code 0. Only restart policies "always" and "unless-stopped"
+// cause a restart on clean exit; "no", "on-failure", and unset do not.
+// For deploy.restart_policy.condition, "any" (and the non-spec but accepted
+// "always" and "unless-stopped") cause a restart on clean exit.
+func restartsOnExit0(project *types.Project, serviceName string) bool {
+	service, err := project.GetService(serviceName)
+	if err != nil {
+		return false
+	}
+	switch service.Restart {
+	case types.RestartPolicyAlways, types.RestartPolicyUnlessStopped:
+		return true
+	}
+	if service.Deploy != nil && service.Deploy.RestartPolicy != nil {
+		switch service.Deploy.RestartPolicy.Condition {
+		case "any", "always", "unless-stopped":
+			return true
+		}
+	}
+	return false
+}
+
 func shouldWaitForDependency(serviceName string, dependencyConfig types.ServiceDependency, project *types.Project) (bool, error) {
 	if dependencyConfig.Condition == types.ServiceConditionStarted {
 		// already managed by InDependencyOrder
@@ -803,6 +834,18 @@ func (s *composeService) getLinks(ctx context.Context, projectName string, servi
 	return links, nil
 }
 
+// containerExitError is returned by isServiceHealthy when a container has exited.
+// It carries the exit code so callers can distinguish clean exits (code 0)
+// from failures without parsing error strings.
+type containerExitError struct {
+	name     string
+	exitCode int
+}
+
+func (e *containerExitError) Error() string {
+	return fmt.Sprintf("container %s exited (%d)", e.name, e.exitCode)
+}
+
 func (s *composeService) isServiceHealthy(ctx context.Context, containers Containers, fallbackRunning bool) (bool, error) {
 	for _, c := range containers {
 		res, err := s.apiClient().ContainerInspect(ctx, c.ID, client.ContainerInspectOptions{})
@@ -813,7 +856,7 @@ func (s *composeService) isServiceHealthy(ctx context.Context, containers Contai
 		name := ctr.Name[1:]
 
 		if ctr.State.Status == container.StateExited {
-			return false, fmt.Errorf("container %s exited (%d)", name, ctr.State.ExitCode)
+			return false, &containerExitError{name: name, exitCode: ctr.State.ExitCode}
 		}
 
 		noHealthcheck := ctr.Config.Healthcheck == nil || (len(ctr.Config.Healthcheck.Test) > 0 && ctr.Config.Healthcheck.Test[0] == "NONE")
diff --git a/pkg/compose/convergence_test.go b/pkg/compose/convergence_test.go
index 901f43ccea..8855dac320 100644
--- a/pkg/compose/convergence_test.go
+++ b/pkg/compose/convergence_test.go
@@ -18,6 +18,7 @@ package compose
 
 import (
 	"context"
+	"errors"
 	"fmt"
 	"net/netip"
 	"strings"
@@ -366,6 +367,34 @@ func TestIsServiceHealthy(t *testing.T) {
 
 		_, err := tested.(*composeService).isServiceHealthy(ctx, containers, true)
 		assert.ErrorContains(t, err, "exited")
+		var exitErr *containerExitError
+		assert.Assert(t, errors.As(err, &exitErr))
+		assert.Equal(t, exitErr.exitCode, 1)
+	})
+
+	t.Run("exited container with exit code 0 returns containerExitError", func(t *testing.T) {
+		containerID := "test-container-id"
+		containers := Containers{
+			{ID: containerID},
+		}
+
+		apiClient.EXPECT().ContainerInspect(ctx, containerID, gomock.Any()).Return(client.ContainerInspectResult{
+			Container: container.InspectResponse{
+				ID:   containerID,
+				Name: "test-container",
+				State: &container.State{
+					Status:   "exited",
+					ExitCode: 0,
+				},
+				Config: &container.Config{},
+			},
+		}, nil)
+
+		_, err := tested.(*composeService).isServiceHealthy(ctx, containers, true)
+		assert.Assert(t, err != nil, "expected error for exited container")
+		var exitErr *containerExitError
+		assert.Assert(t, errors.As(err, &exitErr))
+		assert.Equal(t, exitErr.exitCode, 0)
 	})
 
 	t.Run("healthy container with healthcheck", func(t *testing.T) {
diff --git a/pkg/compose/start_test.go b/pkg/compose/start_test.go
new file mode 100644
index 0000000000..3120d13db4
--- /dev/null
+++ b/pkg/compose/start_test.go
@@ -0,0 +1,109 @@
+/*
+   Copyright 2020 Docker Compose CLI authors
+
+   Licensed under the Apache License, Version 2.0 (the "License");
+   you may not use this file except in compliance with the License.
+   You may obtain a copy of the License at
+
+       http://www.apache.org/licenses/LICENSE-2.0
+
+   Unless required by applicable law or agreed to in writing, software
+   distributed under the License is distributed on an "AS IS" BASIS,
+   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+   See the License for the specific language governing permissions and
+   limitations under the License.
+*/
+
+package compose
+
+import (
+	"testing"
+
+	"github.com/compose-spec/compose-go/v2/types"
+	"gotest.tools/v3/assert"
+)
+
+func TestRestartsOnExit0(t *testing.T) {
+	tests := []struct {
+		name     string
+		service  types.ServiceConfig
+		expected bool
+	}{
+		{
+			name:     "no restart policy",
+			service:  types.ServiceConfig{Name: "init"},
+			expected: false,
+		},
+		{
+			name:     "restart no",
+			service:  types.ServiceConfig{Name: "init", Restart: types.RestartPolicyNo},
+			expected: false,
+		},
+		{
+			name:     "restart on-failure",
+			service:  types.ServiceConfig{Name: "init", Restart: types.RestartPolicyOnFailure},
+			expected: false,
+		},
+		{
+			name:     "restart always",
+			service:  types.ServiceConfig{Name: "web", Restart: types.RestartPolicyAlways},
+			expected: true,
+		},
+		{
+			name:     "restart unless-stopped",
+			service:  types.ServiceConfig{Name: "web", Restart: types.RestartPolicyUnlessStopped},
+			expected: true,
+		},
+		{
+			name: "deploy restart policy condition any",
+			service: types.ServiceConfig{
+				Name: "web",
+				Deploy: &types.DeployConfig{
+					RestartPolicy: &types.RestartPolicy{Condition: "any"},
+				},
+			},
+			expected: true,
+		},
+		{
+			name: "deploy restart policy condition on-failure",
+			service: types.ServiceConfig{
+				Name: "web",
+				Deploy: &types.DeployConfig{
+					RestartPolicy: &types.RestartPolicy{Condition: "on-failure"},
+				},
+			},
+			expected: false,
+		},
+		{
+			name: "deploy restart policy condition none",
+			service: types.ServiceConfig{
+				Name: "web",
+				Deploy: &types.DeployConfig{
+					RestartPolicy: &types.RestartPolicy{Condition: "none"},
+				},
+			},
+			expected: false,
+		},
+		{
+			name: "deploy restart policy condition unless-stopped",
+			service: types.ServiceConfig{
+				Name: "web",
+				Deploy: &types.DeployConfig{
+					RestartPolicy: &types.RestartPolicy{Condition: "unless-stopped"},
+				},
+			},
+			expected: true,
+		},
+	}
+
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			project := &types.Project{
+				Services: types.Services{
+					tt.service.Name: tt.service,
+				},
+			}
+			assert.Equal(t, restartsOnExit0(project, tt.service.Name), tt.expected)
+		})
+	}
+}