diff --git a/apps/mobile/src/features/settings/SettingsScheduledTasksRouteScreen.tsx b/apps/mobile/src/features/settings/SettingsScheduledTasksRouteScreen.tsx
index 3f552c1f0c46c..dd979f3855cbc 100644
--- a/apps/mobile/src/features/settings/SettingsScheduledTasksRouteScreen.tsx
+++ b/apps/mobile/src/features/settings/SettingsScheduledTasksRouteScreen.tsx
@@ -891,21 +891,23 @@ function TaskForm({
               });
             }}
           />
-          <PickerRow
-            label="Model"
-            borderTop
-            value={
-              modelOptions.find(
-                (option) =>
-                  option.selection.instanceId === draft.modelSelection?.instanceId &&
-                  option.selection.model === draft.modelSelection?.model,
-              )?.label ??
-              draft.modelSelection?.model ??
-              (modelOptions.length ? "Choose model" : "No models available")
-            }
-            onPress={() => navigation.navigate("SettingsScheduledTaskModel")}
-            disabled={saving || dictationPending || environmentUnavailable}
-          />
+          {draft.threadId === null ? (
+            <PickerRow
+              label="Model"
+              borderTop
+              value={
+                modelOptions.find(
+                  (option) =>
+                    option.selection.instanceId === draft.modelSelection?.instanceId &&
+                    option.selection.model === draft.modelSelection?.model,
+                )?.label ??
+                draft.modelSelection?.model ??
+                (modelOptions.length ? "Choose model" : "No models available")
+              }
+              onPress={() => navigation.navigate("SettingsScheduledTaskModel")}
+              disabled={saving || dictationPending || environmentUnavailable}
+            />
+          ) : null}
         </SettingsSection>
 
         <SettingsSection
@@ -918,7 +920,9 @@ function TaskForm({
                     ? "Runs continue one conversation."
                     : "Runs share one thread, each in a fresh session without earlier runs' context."
                 }${
-                  draft.threadId === null ? " The first run starts the thread." : ""
+                  draft.threadId === null
+                    ? " The first run starts the thread."
+                    : " Runs use the thread's current model."
                 } Deleting it also deletes this task.`
           }
         >
diff --git a/apps/web/src/components/settings/ScheduledTasksSettings.browser.test.tsx b/apps/web/src/components/settings/ScheduledTasksSettings.browser.test.tsx
index ca8192dd894e3..14f96b43ef850 100644
--- a/apps/web/src/components/settings/ScheduledTasksSettings.browser.test.tsx
+++ b/apps/web/src/components/settings/ScheduledTasksSettings.browser.test.tsx
@@ -215,4 +215,20 @@ describe("ScheduledTasksSettings", () => {
     await expect.element(dialog.getByRole("heading", { name: "New task" })).toBeInTheDocument();
     await expect.element(name).toHaveValue("My draft");
   });
+
+  it("offers the model only while the task is not bound to a thread", async () => {
+    setup();
+    await using _screen = await render(<ScheduledTasksSettings taskId={task.id} />);
+    const dialog = page.getByRole("dialog");
+    const model = dialog.getByRole("button", { name: "Choose model" });
+    await expect
+      .element(dialog.getByText("Each run continues this conversation", { exact: false }))
+      .toBeVisible();
+    await expect.element(model).not.toBeInTheDocument();
+
+    await userEvent.click(dialog.getByRole("combobox", { name: "Destination" }));
+    await userEvent.click(page.getByRole("option", { name: "New thread each run" }));
+
+    await expect.element(model).toBeEnabled();
+  });
 });
diff --git a/apps/web/src/components/settings/ScheduledTasksSettings.tsx b/apps/web/src/components/settings/ScheduledTasksSettings.tsx
index fd4f7702d68ab..464d8536a51d7 100644
--- a/apps/web/src/components/settings/ScheduledTasksSettings.tsx
+++ b/apps/web/src/components/settings/ScheduledTasksSettings.tsx
@@ -1245,7 +1245,7 @@ function ScheduledTaskDestination({
           : "The first run starts a thread with the workspace and model below. Later runs post there, each in a fresh session without earlier runs' context."
         : threadMode === "continue"
           ? "Each run continues this conversation, in its workspace and with its current model."
-          : "Each run starts a fresh session in this thread, without earlier runs' context.";
+          : "Each run starts a fresh session in this thread, with its current model and without earlier runs' context.";
   return (
     <Field label="Destination" htmlFor="scheduled-task-destination">
       {onThreadModeChange ? (
@@ -1766,24 +1766,26 @@ function ScheduledTaskEditorForm({
             />
           </Field>
 
-          <Field label="Model">
-            <div>
-              <ProviderModelPicker
-                environmentId={environmentId}
-                disabled={saving || !connected}
-                activeInstanceId={activeInstanceId}
-                model={activeModel}
-                lockedProvider={null}
-                instanceEntries={instanceEntries}
-                modelOptionsByInstance={modelOptionsByInstance}
-                isComposerOwned={false}
-                triggerClassName={SETTINGS_PICKER_TRIGGER_CLASSNAME}
-                onInstanceModelChange={(instanceId, model) =>
-                  setDraft((current) => ({ ...current, modelKey: `${instanceId}:${model}` }))
-                }
-              />
-            </div>
-          </Field>
+          {draft.threadId === "" ? (
+            <Field label="Model">
+              <div>
+                <ProviderModelPicker
+                  environmentId={environmentId}
+                  disabled={saving || !connected}
+                  activeInstanceId={activeInstanceId}
+                  model={activeModel}
+                  lockedProvider={null}
+                  instanceEntries={instanceEntries}
+                  modelOptionsByInstance={modelOptionsByInstance}
+                  isComposerOwned={false}
+                  triggerClassName={SETTINGS_PICKER_TRIGGER_CLASSNAME}
+                  onInstanceModelChange={(instanceId, model) =>
+                    setDraft((current) => ({ ...current, modelKey: `${instanceId}:${model}` }))
+                  }
+                />
+              </div>
+            </Field>
+          ) : null}
 
           <div className="space-y-3">
             {task?.schedule.type === "interval" &&
diff --git a/docs/user/project-settings.md b/docs/user/project-settings.md
index e0377c11938a5..f65875dca4946 100644
--- a/docs/user/project-settings.md
+++ b/docs/user/project-settings.md
@@ -90,7 +90,8 @@ Under **Destination**, choose where runs go. **New thread each run** keeps every
 run separate. The two one-thread choices start a thread on the first run and post
 later runs there: one continues the same conversation, the other starts each run
 in a fresh session that doesn't see earlier runs, so the thread stays readable
-without the agent's context growing. To move a one-thread task, pick another
+without the agent's context growing. Once the thread exists, runs use its current
+model, so the task no longer offers a model choice. To move a one-thread task, pick another
 thread in its project under **Destination**. Moving such a task to another
 project starts a new thread there on its next run.