diff --git a/src/grid/CallLayout.ts b/src/grid/CallLayout.ts
index c4412677..8f8106de 100644
--- a/src/grid/CallLayout.ts
+++ b/src/grid/CallLayout.ts
@@ -19,22 +19,36 @@ import { ComponentType } from "react";
 
 import { MediaViewModel } from "../state/MediaViewModel";
 import { LayoutProps } from "./Grid";
-import { Alignment } from "../room/InCallView";
 
 export interface Bounds {
   width: number;
   height: number;
 }
 
+export interface Alignment {
+  inline: "start" | "end";
+  block: "start" | "end";
+}
+
+export const defaultSpotlightAlignment: Alignment = {
+  inline: "end",
+  block: "end",
+};
+export const defaultPipAlignment: Alignment = { inline: "end", block: "start" };
+
 export interface CallLayoutInputs {
   /**
    * The minimum bounds of the layout area.
    */
   minBounds: Observable<Bounds>;
   /**
-   * The alignment of the floating tile, if any.
+   * The alignment of the floating spotlight tile, if present.
    */
-  floatingAlignment: BehaviorSubject<Alignment>;
+  spotlightAlignment: BehaviorSubject<Alignment>;
+  /**
+   * The alignment of the small picture-in-picture tile, if present.
+   */
+  pipAlignment: BehaviorSubject<Alignment>;
 }
 
 export interface GridTileModel {
@@ -67,3 +81,68 @@ export interface CallLayoutOutputs<Model> {
 export type CallLayout<Model> = (
   inputs: CallLayoutInputs,
 ) => CallLayoutOutputs<Model>;
+
+export interface GridArrangement {
+  tileWidth: number;
+  tileHeight: number;
+  gap: number;
+  columns: number;
+}
+
+const tileMinHeight = 130;
+const tileMaxAspectRatio = 17 / 9;
+const tileMinAspectRatio = 4 / 3;
+
+/**
+ * Determine the ideal arrangement of tiles into a grid of a particular size.
+ */
+export function arrangeTiles(
+  width: number,
+  minHeight: number,
+  tileCount: number,
+): GridArrangement {
+  // The goal here is to determine the grid size and padding that maximizes
+  // use of screen space for n tiles without making those tiles too small or
+  // too cropped (having an extreme aspect ratio)
+  const gap = width < 800 ? 16 : 20;
+  const tileMinWidth = width < 500 ? 150 : 180;
+
+  let columns = Math.min(
+    // Don't create more columns than we have items for
+    tileCount,
+    // The ideal number of columns is given by a packing of equally-sized
+    // squares into a grid.
+    // width / column = height / row.
+    // columns * rows = number of squares.
+    // ∴ columns = sqrt(width / height * number of squares).
+    // Except we actually want 16:9-ish tiles rather than squares, so we
+    // divide the width-to-height ratio by the target aspect ratio.
+    Math.ceil(Math.sqrt((width / minHeight / tileMaxAspectRatio) * tileCount)),
+  );
+  let rows = Math.ceil(tileCount / columns);
+
+  let tileWidth = (width - (columns - 1) * gap) / columns;
+  let tileHeight = (minHeight - (rows - 1) * gap) / rows;
+
+  // Impose a minimum width and height on the tiles
+  if (tileWidth < tileMinWidth) {
+    // In this case we want the tile width to determine the number of columns,
+    // not the other way around. If we take the above equation for the tile
+    // width (w = (W - (c - 1) * g) / c) and solve for c, we get
+    // c = (W + g) / (w + g).
+    columns = Math.floor((width + gap) / (tileMinWidth + gap));
+    rows = Math.ceil(tileCount / columns);
+    tileWidth = (width - (columns - 1) * gap) / columns;
+    tileHeight = (minHeight - (rows - 1) * gap) / rows;
+  }
+  if (tileHeight < tileMinHeight) tileHeight = tileMinHeight;
+  // Impose a minimum and maximum aspect ratio on the tiles
+  const tileAspectRatio = tileWidth / tileHeight;
+  if (tileAspectRatio > tileMaxAspectRatio)
+    tileWidth = tileHeight * tileMaxAspectRatio;
+  else if (tileAspectRatio < tileMinAspectRatio)
+    tileHeight = tileWidth / tileMinAspectRatio;
+  // TODO: We might now be hitting the minimum height or width limit again
+
+  return { tileWidth, tileHeight, gap, columns };
+}
diff --git a/src/grid/GridLayout.module.css b/src/grid/GridLayout.module.css
index 5e6aa9e1..33edc3be 100644
--- a/src/grid/GridLayout.module.css
+++ b/src/grid/GridLayout.module.css
@@ -17,11 +17,10 @@ limitations under the License.
 .fixed,
 .scrolling {
   margin-inline: var(--inline-content-inset);
+  block-size: 100%;
 }
 
 .scrolling {
-  box-sizing: border-box;
-  block-size: 100%;
   display: flex;
   flex-wrap: wrap;
   justify-content: center;
diff --git a/src/grid/GridLayout.tsx b/src/grid/GridLayout.tsx
index 3861457e..4d499eed 100644
--- a/src/grid/GridLayout.tsx
+++ b/src/grid/GridLayout.tsx
@@ -22,7 +22,12 @@ import { GridLayout as GridLayoutModel } from "../state/CallViewModel";
 import styles from "./GridLayout.module.css";
 import { useReactiveState } from "../useReactiveState";
 import { useInitial } from "../useInitial";
-import { CallLayout, GridTileModel, TileModel } from "./CallLayout";
+import {
+  CallLayout,
+  GridTileModel,
+  TileModel,
+  arrangeTiles,
+} from "./CallLayout";
 import { DragCallback } from "./Grid";
 
 interface GridCSSProperties extends CSSProperties {
@@ -31,13 +36,9 @@ interface GridCSSProperties extends CSSProperties {
   "--height": string;
 }
 
-const slotMinHeight = 130;
-const slotMaxAspectRatio = 17 / 9;
-const slotMinAspectRatio = 4 / 3;
-
 export const makeGridLayout: CallLayout<GridLayoutModel> = ({
   minBounds,
-  floatingAlignment,
+  spotlightAlignment,
 }) => ({
   // The "fixed" (non-scrolling) part of the layout is where the spotlight tile
   // lives
@@ -45,7 +46,7 @@ export const makeGridLayout: CallLayout<GridLayoutModel> = ({
     const { width, height } = useObservableEagerState(minBounds);
     const alignment = useObservableEagerState(
       useInitial(() =>
-        floatingAlignment.pipe(
+        spotlightAlignment.pipe(
           distinctUntilChanged(
             (a1, a2) => a1.block === a2.block && a1.inline === a2.inline,
           ),
@@ -68,7 +69,7 @@ export const makeGridLayout: CallLayout<GridLayoutModel> = ({
 
     const onDragSpotlight: DragCallback = useCallback(
       ({ xRatio, yRatio }) =>
-        floatingAlignment.next({
+        spotlightAlignment.next({
           block: yRatio < 0.5 ? "start" : "end",
           inline: xRatio < 0.5 ? "start" : "end",
         }),
@@ -76,12 +77,7 @@ export const makeGridLayout: CallLayout<GridLayoutModel> = ({
     );
 
     return (
-      <div
-        ref={ref}
-        className={styles.fixed}
-        data-generation={generation}
-        style={{ height }}
-      >
+      <div ref={ref} className={styles.fixed} data-generation={generation}>
         {tileModel && (
           <Slot
             className={styles.slot}
@@ -99,57 +95,10 @@ export const makeGridLayout: CallLayout<GridLayoutModel> = ({
   // The scrolling part of the layout is where all the grid tiles live
   scrolling: forwardRef(function GridLayout({ model, Slot }, ref) {
     const { width, height: minHeight } = useObservableEagerState(minBounds);
-
-    // The goal here is to determine the grid size and padding that maximizes
-    // use of screen space for n tiles without making those tiles too small or
-    // too cropped (having an extreme aspect ratio)
-    const [gap, slotWidth, slotHeight] = useMemo(() => {
-      const gap = width < 800 ? 16 : 20;
-      const slotMinWidth = width < 500 ? 150 : 180;
-
-      let columns = Math.min(
-        // Don't create more columns than we have items for
-        model.grid.length,
-        // The ideal number of columns is given by a packing of equally-sized
-        // squares into a grid.
-        // width / column = height / row.
-        // columns * rows = number of squares.
-        // ∴ columns = sqrt(width / height * number of squares).
-        // Except we actually want 16:9-ish slots rather than squares, so we
-        // divide the width-to-height ratio by the target aspect ratio.
-        Math.ceil(
-          Math.sqrt(
-            (width / minHeight / slotMaxAspectRatio) * model.grid.length,
-          ),
-        ),
-      );
-      let rows = Math.ceil(model.grid.length / columns);
-
-      let slotWidth = (width - (columns - 1) * gap) / columns;
-      let slotHeight = (minHeight - (rows - 1) * gap) / rows;
-
-      // Impose a minimum width and height on the slots
-      if (slotWidth < slotMinWidth) {
-        // In this case we want the slot width to determine the number of columns,
-        // not the other way around. If we take the above equation for the slot
-        // width (w = (W - (c - 1) * g) / c) and solve for c, we get
-        // c = (W + g) / (w + g).
-        columns = Math.floor((width + gap) / (slotMinWidth + gap));
-        rows = Math.ceil(model.grid.length / columns);
-        slotWidth = (width - (columns - 1) * gap) / columns;
-        slotHeight = (minHeight - (rows - 1) * gap) / rows;
-      }
-      if (slotHeight < slotMinHeight) slotHeight = slotMinHeight;
-      // Impose a minimum and maximum aspect ratio on the slots
-      const slotAspectRatio = slotWidth / slotHeight;
-      if (slotAspectRatio > slotMaxAspectRatio)
-        slotWidth = slotHeight * slotMaxAspectRatio;
-      else if (slotAspectRatio < slotMinAspectRatio)
-        slotHeight = slotWidth / slotMinAspectRatio;
-      // TODO: We might now be hitting the minimum height or width limit again
-
-      return [gap, slotWidth, slotHeight];
-    }, [width, minHeight, model.grid.length]);
+    const { gap, tileWidth, tileHeight } = useMemo(
+      () => arrangeTiles(width, minHeight, model.grid.length),
+      [width, minHeight, model.grid.length],
+    );
 
     const [generation] = useReactiveState<number>(
       (prev) => (prev === undefined ? 0 : prev + 1),
@@ -170,8 +119,8 @@ export const makeGridLayout: CallLayout<GridLayoutModel> = ({
           {
             width,
             "--gap": `${gap}px`,
-            "--width": `${Math.floor(slotWidth)}px`,
-            "--height": `${Math.floor(slotHeight)}px`,
+            "--width": `${Math.floor(tileWidth)}px`,
+            "--height": `${Math.floor(tileHeight)}px`,
           } as GridCSSProperties
         }
       >
diff --git a/src/grid/OneOnOneLayout.module.css b/src/grid/OneOnOneLayout.module.css
new file mode 100644
index 00000000..0d2ad4ff
--- /dev/null
+++ b/src/grid/OneOnOneLayout.module.css
@@ -0,0 +1,56 @@
+/*
+Copyright 2024 New Vector Ltd
+
+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.
+*/
+
+.layer {
+  margin-inline: var(--inline-content-inset);
+  block-size: 100%;
+  display: grid;
+  place-items: center;
+}
+
+.container {
+  position: relative;
+}
+
+.local {
+  position: absolute;
+  inline-size: 180px;
+  block-size: 135px;
+  inset: var(--cpd-space-4x);
+}
+
+.spotlight {
+  position: absolute;
+  inline-size: 404px;
+  block-size: 233px;
+  inset: -12px;
+}
+
+.slot[data-block-alignment="start"] {
+  inset-block-end: unset;
+}
+
+.slot[data-block-alignment="end"] {
+  inset-block-start: unset;
+}
+
+.slot[data-inline-alignment="start"] {
+  inset-inline-end: unset;
+}
+
+.slot[data-inline-alignment="end"] {
+  inset-inline-start: unset;
+}
diff --git a/src/grid/OneOnOneLayout.tsx b/src/grid/OneOnOneLayout.tsx
new file mode 100644
index 00000000..2eac1b7e
--- /dev/null
+++ b/src/grid/OneOnOneLayout.tsx
@@ -0,0 +1,132 @@
+/*
+Copyright 2024 New Vector Ltd
+
+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.
+*/
+
+import { forwardRef, useCallback, useMemo } from "react";
+import { useObservableEagerState } from "observable-hooks";
+import classNames from "classnames";
+
+import { OneOnOneLayout as OneOnOneLayoutModel } from "../state/CallViewModel";
+import {
+  CallLayout,
+  GridTileModel,
+  SpotlightTileModel,
+  arrangeTiles,
+} from "./CallLayout";
+import { useReactiveState } from "../useReactiveState";
+import styles from "./OneOnOneLayout.module.css";
+import { DragCallback } from "./Grid";
+
+export const makeOneOnOneLayout: CallLayout<OneOnOneLayoutModel> = ({
+  minBounds,
+  spotlightAlignment,
+  pipAlignment,
+}) => ({
+  fixed: forwardRef(function OneOnOneLayoutFixed({ model, Slot }, ref) {
+    const { width, height } = useObservableEagerState(minBounds);
+    const spotlightAlignmentValue = useObservableEagerState(spotlightAlignment);
+
+    const [generation] = useReactiveState<number>(
+      (prev) => (prev === undefined ? 0 : prev + 1),
+      [width, height, model.spotlight === undefined, spotlightAlignmentValue],
+    );
+
+    const spotlightTileModel: SpotlightTileModel | undefined = useMemo(
+      () =>
+        model.spotlight && {
+          type: "spotlight",
+          vms: model.spotlight,
+          maximised: false,
+        },
+      [model.spotlight],
+    );
+
+    const onDragSpotlight: DragCallback = useCallback(
+      ({ xRatio, yRatio }) =>
+        spotlightAlignment.next({
+          block: yRatio < 0.5 ? "start" : "end",
+          inline: xRatio < 0.5 ? "start" : "end",
+        }),
+      [],
+    );
+
+    return (
+      <div ref={ref} data-generation={generation} className={styles.layer}>
+        {spotlightTileModel && (
+          <Slot
+            className={classNames(styles.slot, styles.spotlight)}
+            id="spotlight"
+            model={spotlightTileModel}
+            onDrag={onDragSpotlight}
+            data-block-alignment={spotlightAlignmentValue.block}
+            data-inline-alignment={spotlightAlignmentValue.inline}
+          />
+        )}
+      </div>
+    );
+  }),
+
+  scrolling: forwardRef(function OneOnOneLayoutScrolling({ model, Slot }, ref) {
+    const { width, height } = useObservableEagerState(minBounds);
+    const pipAlignmentValue = useObservableEagerState(pipAlignment);
+    const { tileWidth, tileHeight } = useMemo(
+      () => arrangeTiles(width, height, 1),
+      [width, height],
+    );
+
+    const [generation] = useReactiveState<number>(
+      (prev) => (prev === undefined ? 0 : prev + 1),
+      [width, height, pipAlignmentValue],
+    );
+
+    const remoteTileModel: GridTileModel = useMemo(
+      () => ({ type: "grid", vm: model.remote }),
+      [model.remote],
+    );
+    const localTileModel: GridTileModel = useMemo(
+      () => ({ type: "grid", vm: model.local }),
+      [model.local],
+    );
+
+    const onDragLocalTile: DragCallback = useCallback(
+      ({ xRatio, yRatio }) =>
+        pipAlignment.next({
+          block: yRatio < 0.5 ? "start" : "end",
+          inline: xRatio < 0.5 ? "start" : "end",
+        }),
+      [],
+    );
+
+    return (
+      <div ref={ref} data-generation={generation} className={styles.layer}>
+        <Slot
+          id={remoteTileModel.vm.id}
+          model={remoteTileModel}
+          className={styles.container}
+          style={{ width: tileWidth, height: tileHeight }}
+        >
+          <Slot
+            className={classNames(styles.slot, styles.local)}
+            id={localTileModel.vm.id}
+            model={localTileModel}
+            onDrag={onDragLocalTile}
+            data-block-alignment={pipAlignmentValue.block}
+            data-inline-alignment={pipAlignmentValue.inline}
+          />
+        </Slot>
+      </div>
+    );
+  }),
+});
diff --git a/src/grid/SpotlightLayout.module.css b/src/grid/SpotlightLayout.module.css
index af43216c..d58a95a1 100644
--- a/src/grid/SpotlightLayout.module.css
+++ b/src/grid/SpotlightLayout.module.css
@@ -16,6 +16,7 @@ limitations under the License.
 
 .layer {
   margin-inline: var(--inline-content-inset);
+  block-size: 100%;
   display: grid;
   --grid-gap: 20px;
   gap: 30px;
@@ -30,10 +31,6 @@ limitations under the License.
   grid-template-rows: minmax(1fr, auto);
 }
 
-.scrolling {
-  block-size: 100%;
-}
-
 .spotlight {
   container: spotlight / size;
   display: grid;
diff --git a/src/grid/SpotlightLayout.tsx b/src/grid/SpotlightLayout.tsx
index 3e07a0b2..9ddbce10 100644
--- a/src/grid/SpotlightLayout.tsx
+++ b/src/grid/SpotlightLayout.tsx
@@ -69,10 +69,8 @@ export const makeSpotlightLayout: CallLayout<SpotlightLayoutModel> = ({
         ref={ref}
         data-generation={generation}
         data-orientation={layout.orientation}
-        className={classNames(styles.layer, styles.fixed)}
-        style={
-          { "--grid-columns": layout.gridColumns, height } as GridCSSProperties
-        }
+        className={styles.layer}
+        style={{ "--grid-columns": layout.gridColumns } as GridCSSProperties}
       >
         <div className={styles.spotlight}>
           <Slot className={styles.slot} id="spotlight" model={tileModel} />
@@ -102,7 +100,7 @@ export const makeSpotlightLayout: CallLayout<SpotlightLayoutModel> = ({
         ref={ref}
         data-generation={generation}
         data-orientation={layout.orientation}
-        className={classNames(styles.layer, styles.scrolling)}
+        className={styles.layer}
         style={{ "--grid-columns": layout.gridColumns } as GridCSSProperties}
       >
         <div
diff --git a/src/room/InCallView.tsx b/src/room/InCallView.tsx
index bab24991..90791de6 100644
--- a/src/room/InCallView.tsx
+++ b/src/room/InCallView.tsx
@@ -87,17 +87,17 @@ import { EncryptionSystem } from "../e2ee/sharedKeyManagement";
 import { E2eeType } from "../e2ee/e2eeType";
 import { makeGridLayout } from "../grid/GridLayout";
 import { makeSpotlightLayout } from "../grid/SpotlightLayout";
-import { CallLayout, GridTileModel, TileModel } from "../grid/CallLayout";
+import {
+  CallLayout,
+  GridTileModel,
+  TileModel,
+  defaultPipAlignment,
+  defaultSpotlightAlignment,
+} from "../grid/CallLayout";
+import { makeOneOnOneLayout } from "../grid/OneOnOneLayout";
 
 const canScreenshare = "getDisplayMedia" in (navigator.mediaDevices ?? {});
 
-export interface Alignment {
-  inline: "start" | "end";
-  block: "start" | "end";
-}
-
-const defaultAlignment: Alignment = { inline: "end", block: "end" };
-
 const dummySpotlightItem = {
   id: "spotlight",
 } as TileDescriptor<MediaViewModel>;
@@ -321,8 +321,11 @@ export const InCallView: FC<InCallViewProps> = ({
   );
   const gridBoundsObservable = useObservable(gridBounds);
 
-  const floatingAlignment = useInitial(
-    () => new BehaviorSubject(defaultAlignment),
+  const spotlightAlignment = useInitial(
+    () => new BehaviorSubject(defaultSpotlightAlignment),
+  );
+  const pipAlignment = useInitial(
+    () => new BehaviorSubject(defaultPipAlignment),
   );
 
   const layoutSystem = useObservableEagerState(
@@ -334,11 +337,14 @@ export const InCallView: FC<InCallViewProps> = ({
             makeLayout = makeGridLayout as CallLayout<Layout>;
           else if (l.type === "spotlight")
             makeLayout = makeSpotlightLayout as CallLayout<Layout>;
+          else if (l.type === "one-on-one")
+            makeLayout = makeOneOnOneLayout as CallLayout<Layout>;
           else return null; // Not yet implemented
 
           return makeLayout({
             minBounds: gridBoundsObservable,
-            floatingAlignment,
+            spotlightAlignment,
+            pipAlignment,
           });
         }),
       ),
@@ -491,7 +497,10 @@ export const InCallView: FC<InCallViewProps> = ({
           />
           <Grid
             className={styles.fixedGrid}
-            style={{ insetBlockStart: headerBounds.bottom }}
+            style={{
+              insetBlockStart: headerBounds.bottom,
+              height: gridBounds.height,
+            }}
             model={layout}
             Layout={layoutSystem.fixed}
             Tile={Tile}