diff --git a/README.md b/README.md
index 2e71f53..1d6307d 100644
--- a/README.md
+++ b/README.md
@@ -46,7 +46,7 @@ Two ways to have it. `--runtime docker` pulls the published image, and is what w
 
 Both put the index in the same place, `$XDG_DATA_HOME/sourceant`, so it does not matter which one indexed it. The container runs as whoever installed, so what it writes there belongs to them.
 
-`sourceant ui` starts the agent and opens the view.
+`sourceant ui` starts the agent and opens the view. `sourceant stop` shuts down the agent and its core without removing the index or configuration. Stopping requires an agent with stop support.
 
 | Variable | Default | Meaning |
 |---|---|---|
@@ -59,6 +59,7 @@ Both put the index in the same place, `$XDG_DATA_HOME/sourceant`, so it does not
 | Command | What it does |
 |---|---|
 | `sourceant setup` | Put the agent and a core on this machine |
+| `sourceant stop` | Stop the agent and its Python core or Docker container |
 | `sourceant status` | Whether the agent and the indexer are running |
 | `sourceant repos` | Repositories indexed on this machine |
 | `sourceant graph <repository>` | What the indexer found in one of them |
diff --git a/internal/agent/client.go b/internal/agent/client.go
index 9a6dc0e..920906e 100644
--- a/internal/agent/client.go
+++ b/internal/agent/client.go
@@ -8,12 +8,14 @@ package agent
 import (
 	"context"
 	"encoding/json"
+	"errors"
 	"fmt"
 	"io"
 	"net/http"
 	"net/url"
 	"strconv"
 	"strings"
+	"syscall"
 	"time"
 )
 
@@ -80,6 +82,11 @@ func (e *Unreachable) Error() string {
 
 func (e *Unreachable) Unwrap() error { return e.Cause }
 
+func IsConnectionRefused(err error) bool {
+	var unreachable *Unreachable
+	return errors.As(err, &unreachable) && errors.Is(unreachable.Cause, syscall.ECONNREFUSED)
+}
+
 // Client talks to one agent.
 type Client struct {
 	baseURL string
@@ -169,3 +176,30 @@ func detail(body []byte) string {
 	}
 	return strings.TrimSpace(string(body))
 }
+
+func (c *Client) Stop(ctx context.Context) error {
+	req, err := http.NewRequestWithContext(ctx, http.MethodPost, c.baseURL+"/api/stop", nil)
+	if err != nil {
+		return err
+	}
+	req.Header.Set("X-Sourceant-Client", "cli")
+	req.Header.Set("Accept", "application/json")
+	resp, err := c.http.Do(req)
+	if err != nil {
+		return &Unreachable{BaseURL: c.baseURL, Cause: err}
+	}
+	defer func() { _ = resp.Body.Close() }()
+	switch resp.StatusCode {
+	case http.StatusNoContent:
+		return nil
+	case http.StatusOK, http.StatusNotFound, http.StatusMethodNotAllowed:
+		// Only 204 acknowledges shutdown; a generic 200 does not confirm it.
+		return &Error{StatusCode: resp.StatusCode, Detail: "this agent does not support stop; update it with sourceant setup"}
+	default:
+		body, err := io.ReadAll(resp.Body)
+		if err != nil {
+			return err
+		}
+		return &Error{StatusCode: resp.StatusCode, Detail: detail(body)}
+	}
+}
diff --git a/internal/command/root.go b/internal/command/root.go
index fd32991..570294b 100644
--- a/internal/command/root.go
+++ b/internal/command/root.go
@@ -52,6 +52,7 @@ func Run(args []string, stdout, stderr io.Writer) int {
 	root.PersistentFlags().BoolVar(&opts.asJSON, "json", false, "Print the agent's answer as JSON")
 
 	root.AddCommand(
+		stopCommand(opts),
 		setupCommand(),
 		statusCommand(opts),
 		reposCommand(opts),
diff --git a/internal/command/stop.go b/internal/command/stop.go
new file mode 100644
index 0000000..d928c9a
--- /dev/null
+++ b/internal/command/stop.go
@@ -0,0 +1,27 @@
+package command
+
+import (
+	"fmt"
+
+	"github.com/sourceant/cli/internal/agent"
+	"github.com/spf13/cobra"
+)
+
+func stopCommand(opts *options) *cobra.Command {
+	return &cobra.Command{
+		Use:   "stop",
+		Short: "Stop the agent and its core",
+		Args:  cobra.NoArgs,
+		RunE: func(cmd *cobra.Command, _ []string) error {
+			if err := opts.client().Stop(cmd.Context()); err != nil {
+				if agent.IsConnectionRefused(err) {
+					_, _ = fmt.Fprintln(cmd.OutOrStdout(), "SourceAnt is already stopped.")
+					return nil
+				}
+				return fmt.Errorf("could not stop SourceAnt: %w", err)
+			}
+			_, _ = fmt.Fprintln(cmd.OutOrStdout(), "Stopped SourceAnt.")
+			return nil
+		},
+	}
+}
diff --git a/internal/command/stop_test.go b/internal/command/stop_test.go
new file mode 100644
index 0000000..e8e3d44
--- /dev/null
+++ b/internal/command/stop_test.go
@@ -0,0 +1,60 @@
+package command
+
+import (
+	"bytes"
+	"net/http"
+	"net/http/httptest"
+	"strings"
+	"testing"
+)
+
+func TestStopCommand(t *testing.T) {
+	for _, status := range []int{http.StatusNoContent, http.StatusOK, http.StatusNotFound, http.StatusMethodNotAllowed, http.StatusInternalServerError} {
+		server := httptest.NewServer(http.HandlerFunc(func(w http.ResponseWriter, r *http.Request) {
+			if r.Method != "POST" || r.URL.Path != "/api/stop" || r.Header.Get("X-Sourceant-Client") != "cli" || r.Header.Get("Accept") != "application/json" {
+				t.Errorf("unexpected stop request: %s %s", r.Method, r.URL)
+			}
+			w.WriteHeader(status)
+		}))
+		var out, stderr bytes.Buffer
+		code := Run([]string{"--agent", server.URL, "stop"}, &out, &stderr)
+		server.Close()
+		if (code == 0) != (status == http.StatusNoContent) {
+			t.Fatalf("status=%d code=%d: %s", status, code, stderr.String())
+		}
+		if status == http.StatusOK || status == http.StatusNotFound || status == http.StatusMethodNotAllowed {
+			if !strings.Contains(stderr.String(), "this agent does not support stop; update it with sourceant setup") {
+				t.Fatal(stderr.String())
+			}
+		}
+		if code == 0 && !strings.Contains(out.String(), "Stopped SourceAnt.") {
+			t.Fatal(out.String())
+		}
+	}
+}
+
+func TestStopAlreadyStopped(t *testing.T) {
+	server := httptest.NewServer(http.NotFoundHandler())
+	server.Close()
+	var out, stderr bytes.Buffer
+	if Run([]string{"--agent", server.URL, "stop"}, &out, &stderr) != 0 {
+		t.Fatal(stderr.String())
+	}
+	if !strings.Contains(out.String(), "already stopped") {
+		t.Fatal(out.String())
+	}
+}
+
+func TestStopTimeoutIsNotAlreadyStopped(t *testing.T) {
+	server := httptest.NewServer(http.HandlerFunc(func(w http.ResponseWriter, r *http.Request) {
+		<-r.Context().Done()
+	}))
+	defer server.Close()
+	var out, stderr bytes.Buffer
+	if Run([]string{"--agent", server.URL, "--timeout", "20ms", "stop"}, &out, &stderr) == 0 {
+		t.Fatal("a timed-out stop request succeeded")
+	}
+	if strings.Contains(out.String(), "already stopped") || stderr.Len() == 0 {
+		t.Fatalf("stdout=%s stderr=%s", out.String(), stderr.String())
+	}
+}