diff --git a/src/pages/admin/bots/[bot_id]/(partials)/user-message-copy.tsx b/src/pages/admin/bots/[bot_id]/(partials)/user-message-copy.tsx
new file mode 100644
index 0000000..d747880
--- /dev/null
+++ b/src/pages/admin/bots/[bot_id]/(partials)/user-message-copy.tsx
@@ -0,0 +1,15 @@
+import CopyMessageButton from "./copy-message-button";
+
+type Props = {
+    text: string;
+};
+
+/**
+ * One message's copy button, in the row under a user group beside its
+ * timestamp. A message with no text renders nothing at all.
+ */
+export default function UserMessageCopy({ text }: Props) {
+    if (!text.trim()) return null;
+
+    return <CopyMessageButton text={text} />;
+}
diff --git a/src/pages/admin/bots/[bot_id]/(partials)/user-message-group.tsx b/src/pages/admin/bots/[bot_id]/(partials)/user-message-group.tsx
index a93e377..71e4089 100644
--- a/src/pages/admin/bots/[bot_id]/(partials)/user-message-group.tsx
+++ b/src/pages/admin/bots/[bot_id]/(partials)/user-message-group.tsx
@@ -1,7 +1,10 @@
+import Row from "@moduletrace/twui/layout/Row";
 import Stack from "@moduletrace/twui/layout/Stack";
 import type { BotWithLastMessage } from "@/src/types";
+import copyableMessages from "../(utils)/copyable-messages";
 import type { MessageGroup } from "../(utils)/group-messages";
 import UserMessage from "./user-message";
+import UserMessageCopy from "./user-message-copy";
 import GroupTimestamp from "./group-timestamp";
 
 type Props = {
@@ -10,16 +13,24 @@ type Props = {
 };
 
 /**
- * Right-aligned ink bubbles (each message's files above it), one
- * timestamp under the group.
+ * Right-aligned ink bubbles (each message's files above it), then one
+ * row under the group: a copy button per message with text, left of the
+ * group's time.
  */
 export default function UserMessageGroup({ bot, group }: Props) {
+    const copyable = copyableMessages({ messages: group.messages });
+
     return (
         <Stack className="w-full gap-1! items-end">
             {group.messages.map((message) => (
                 <UserMessage key={message.id} message={message} bot_name={bot.name || "the bot"} />
             ))}
-            <GroupTimestamp at={group.at} />
+            <Row className="gap-3! items-center">
+                {copyable.map((message) => (
+                    <UserMessageCopy key={message.id} text={message.text || ""} />
+                ))}
+                <GroupTimestamp at={group.at} />
+            </Row>
         </Stack>
     );
 }
diff --git a/src/pages/admin/bots/[bot_id]/(partials)/user-message.tsx b/src/pages/admin/bots/[bot_id]/(partials)/user-message.tsx
index 2aa32e5..b7fd91c 100644
--- a/src/pages/admin/bots/[bot_id]/(partials)/user-message.tsx
+++ b/src/pages/admin/bots/[bot_id]/(partials)/user-message.tsx
@@ -1,8 +1,6 @@
 import { memo } from "react";
-import Row from "@moduletrace/twui/layout/Row";
 import Stack from "@moduletrace/twui/layout/Stack";
 import type { BotMessageWithAttachments } from "@/src/types";
-import CopyMessageButton from "./copy-message-button";
 import MessageAttachments from "./message-attachments";
 import MessageReactions from "./message-reactions";
 import MessageReplyQuote from "./message-reply-quote";
@@ -17,7 +15,8 @@ type Props = {
  * One user message: the quoted message it answers, its files, then its
  * text (a file-only message has no bubble) and the bot's reactions to it.
  * The user doesn't reply to or react to their own messages, but they can
- * copy one. Memoized, like `BotMessageLine`.
+ * copy one: the group's copy buttons sit beside its timestamp, in
+ * `UserMessageGroup`. Memoized, like `BotMessageLine`.
  */
 function UserMessage({ message, bot_name }: Props) {
     return (
@@ -37,11 +36,6 @@ function UserMessage({ message, bot_name }: Props) {
                     reactions={message.reactions}
                 />
             ) : null}
-            {message.text ? (
-                <Row className="gap-3! items-center">
-                    <CopyMessageButton text={message.text} />
-                </Row>
-            ) : null}
         </Stack>
     );
 }
diff --git a/src/pages/admin/bots/[bot_id]/(utils)/copyable-messages.test.ts b/src/pages/admin/bots/[bot_id]/(utils)/copyable-messages.test.ts
new file mode 100644
index 0000000..b9f7f3a
--- /dev/null
+++ b/src/pages/admin/bots/[bot_id]/(utils)/copyable-messages.test.ts
@@ -0,0 +1,27 @@
+import { describe, expect, test } from "bun:test";
+import type { BotMessageWithAttachments } from "@/src/types";
+import copyableMessages from "./copyable-messages";
+
+function message(text?: string): BotMessageWithAttachments {
+    return { id: 1, author: "user", text } as BotMessageWithAttachments;
+}
+
+describe("copyableMessages", () => {
+    test("keeps the messages that have text", () => {
+        const kept = copyableMessages({
+            messages: [message("hello"), message(undefined), message("hi")],
+        });
+
+        expect(kept.map((one) => one.text)).toEqual(["hello", "hi"]);
+    });
+
+    test("drops text that is only whitespace", () => {
+        expect(copyableMessages({ messages: [message("   ")] })).toEqual([]);
+    });
+
+    test("a group with no text has nothing to copy", () => {
+        expect(copyableMessages({ messages: [message(), message()] })).toEqual(
+            [],
+        );
+    });
+});
diff --git a/src/pages/admin/bots/[bot_id]/(utils)/copyable-messages.ts b/src/pages/admin/bots/[bot_id]/(utils)/copyable-messages.ts
new file mode 100644
index 0000000..d1f986b
--- /dev/null
+++ b/src/pages/admin/bots/[bot_id]/(utils)/copyable-messages.ts
@@ -0,0 +1,14 @@
+import type { BotMessageWithAttachments } from "@/src/types";
+
+/**
+ * The messages of a group that can be copied: a file-only message has no
+ * text, and its copy button renders nothing, so it would only leave a
+ * gap in the row.
+ */
+export default function copyableMessages({
+    messages,
+}: {
+    messages: BotMessageWithAttachments[];
+}): BotMessageWithAttachments[] {
+    return messages.filter((message) => Boolean(message.text?.trim()));
+}