diff --git a/src/components/CallView/CallView.vue b/src/components/CallView/CallView.vue
index a72784c9020..3608ed5f9dc 100644
--- a/src/components/CallView/CallView.vue
+++ b/src/components/CallView/CallView.vue
@@ -34,7 +34,7 @@
 						:model="selectedCallParticipantModel"
 						:sharedData="sharedDatas[selectedVideoPeerId]"
 						:showTalkingHighlight="false"
-						:isOneToOne="isOneToOne"
+						:isFullPage="showFullPage"
 						isGrid
 						isBig
 						fitVideo />
@@ -77,7 +77,6 @@
 						:models="promotedSpeakerModels"
 						:sharedDatas="sharedDatas"
 						:showVideoOverlay="showVideoOverlay"
-						:isOneToOne="isOneToOne"
 						@selectVideo="handleSelectVideo" />
 					<!-- Promoted "autopilot" mode -->
 					<VideoVue
@@ -91,7 +90,7 @@
 						isGrid
 						fitVideo
 						isBig
-						:isOneToOne="isOneToOne"
+						:isFullPage="showFullPage"
 						:isSidebar="isSidebar"
 						@forcePromoteVideo="forcePromotedModel = $event" />
 					<!-- presenter overlay -->
@@ -451,12 +450,13 @@ export default {
 			return this.selectedVideoPeerId !== null && !this.screens.includes(this.selectedVideoPeerId)
 		},
 
-		isOneToOne() {
-			return this.callParticipantModels.length === 1
-		},
-
+		// Whether the promoted video covers the whole call view, with the stripe
+		// floating over it rather than taking room of its own. A promoted area
+		// held by a single participant is laid out that way, and so is one with
+		// nobody in it yet.
 		showFullPage() {
-			return this.isOneToOne && !(this.showLocalScreen || this.showRemoteScreen || this.showSelectedScreen)
+			return this.callParticipantModels.length <= 1
+				&& !(this.showLocalScreen || this.showRemoteScreen || this.showSelectedScreen)
 		},
 
 		hasLocalVideo() {
diff --git a/src/components/CallView/Grid/SpeakersGrid.vue b/src/components/CallView/Grid/SpeakersGrid.vue
index d9d595c804e..63c8fbdd750 100644
--- a/src/components/CallView/Grid/SpeakersGrid.vue
+++ b/src/components/CallView/Grid/SpeakersGrid.vue
@@ -23,8 +23,6 @@ const props = defineProps<{
 	sharedDatas: Record<string, object>
 	/** Whether the video overlay is currently shown */
 	showVideoOverlay?: boolean
-	/** Whether the call is a one to one conversation */
-	isOneToOne?: boolean
 }>()
 
 const emit = defineEmits<{
@@ -101,7 +99,6 @@ function tileStyle(index: number) {
 				:model="model"
 				:sharedData="sharedDatas[model.attributes.peerId]"
 				:showVideoOverlay="showVideoOverlay"
-				:isOneToOne="isOneToOne"
 				isGrid
 				fitVideo
 				@clickVideo="emit('selectVideo', model.attributes.peerId)" />
diff --git a/src/components/CallView/Grid/StripeControls.vue b/src/components/CallView/Grid/StripeControls.vue
index bedb241903b..9ccabb76ebd 100644
--- a/src/components/CallView/Grid/StripeControls.vue
+++ b/src/components/CallView/Grid/StripeControls.vue
@@ -122,7 +122,7 @@ const toggleLabel = computed(() => props.isOpen
 	align-items: center;
 	gap: var(--default-grid-baseline);
 	width: fit-content;
-	padding-block-start: var(--default-grid-baseline);
+	padding-block-start: var(--grid-gap);
 	// Barely there while the call is not being looked at, as they sit over the
 	// tiles, and in their own color as soon as it is
 	opacity: .4;
diff --git a/src/components/CallView/Grid/VideosGrid.vue b/src/components/CallView/Grid/VideosGrid.vue
index 2046e4d993c..cd8717b15fe 100644
--- a/src/components/CallView/Grid/VideosGrid.vue
+++ b/src/components/CallView/Grid/VideosGrid.vue
@@ -173,6 +173,7 @@ import {
 	getHalfColumnCount,
 	getHalfColumnMaxWidth,
 	getHalfColumnMinWidth,
+	getJustifyContent,
 	GRID_GAP,
 	TARGET_ASPECT_RATIO,
 	TILE_COLUMN_SPAN,
@@ -465,8 +466,14 @@ export default {
 				gridTemplateColumns: `repeat(${getHalfColumnCount(columns)}, ${halfColumnWidth})`,
 				gridTemplateRows: `repeat(${rows}, minmax(${this.dpiAwareMinHeight}px, 1fr))`,
 				// The columns no longer take the whole width once they are
-				// capped, so the grid itself has to center them
-				justifyContent: 'center',
+				// capped, so the grid itself has to place them
+				justifyContent: getJustifyContent({
+					isStripe: this.isStripe,
+					totalTiles: this.totalTiles,
+					// The local video is laid out after the remote tiles, so it
+					// is the only tile of the grid when no remote one is shown
+					isLocalVideoAlone: !this.noLocalVideoReserve && this.displayedVideos.length === 0,
+				}),
 			}
 		},
 
@@ -614,6 +621,7 @@ export default {
 
 	&--stripe {
 		height: var(--stripe-height);
+		margin-block-start: var(--grid-gap);
 	}
 }
 
@@ -669,6 +677,22 @@ export default {
 	// Kept out of the grid itself, whose measured height is the height of its
 	// tiles
 	padding-block: var(--grid-gap);
+	// Keeps the tiles off the rounded corners of the card
+	padding-inline: var(--grid-gap);
+
+	// The card the tiles sit on
+	.grid-main-wrapper:not(.overlap) & {
+		background-color: #262626;
+		border-radius: var(--border-radius-container);
+	}
+
+	// A stripe overlapping the promoted video takes no card of its own, which
+	// would band that video across: its tiles - the self camera, the only one
+	// left in a one to one call - are lifted off the call by a shadow instead
+	.overlap & :deep(.localVideoContainer),
+	.overlap & :deep(.video-container-grid) {
+		box-shadow: 0 0px 10px rgba(0, 0, 0, 0.5);
+	}
 }
 
 .dev-mode-video {
@@ -744,15 +768,15 @@ export default {
 
 .stripe-controls-position {
 	position: absolute;
-	top: var(--grid-gap);
-	inset-inline-end: var(--grid-gap);
+	top: calc(var(--default-grid-baseline) * 3);
+	inset-inline-end: calc(var(--default-grid-baseline) * 3);
 	z-index: 2;
 	transition: top var(--animation-slow) ease-in-out;
 
 	// A collapsed stripe holds no tile to sit over, and no room of its own to
 	// sit in, so the controls take the room above it
 	&--collapsed {
-		top: calc(-1 * (var(--clickable-area-small) + var(--default-grid-baseline) + var(--grid-gap)));
+		top: calc(-1 * (var(--clickable-area-small) + var(--grid-gap) + var(--grid-gap)));
 	}
 }
 
diff --git a/src/components/CallView/Grid/gridLayout.spec.ts b/src/components/CallView/Grid/gridLayout.spec.ts
index 34e3d943198..5e059ca351c 100644
--- a/src/components/CallView/Grid/gridLayout.spec.ts
+++ b/src/components/CallView/Grid/gridLayout.spec.ts
@@ -11,6 +11,7 @@ import {
 	getHalfColumnCount,
 	getHalfColumnMaxWidth,
 	getHalfColumnMinWidth,
+	getJustifyContent,
 	getMinTileHeight,
 	getMinTileWidth,
 	GRID_GAP,
@@ -342,4 +343,25 @@ describe('gridLayout', () => {
 			}
 		})
 	})
+
+	describe('getJustifyContent', () => {
+		test('centers the tiles of the grid', () => {
+			expect(getJustifyContent({ isStripe: false, totalTiles: 1, isLocalVideoAlone: true })).toBe('center')
+			expect(getJustifyContent({ isStripe: false, totalTiles: 5, isLocalVideoAlone: false })).toBe('center')
+		})
+
+		test('centers the tiles of a stripe holding several of them', () => {
+			expect(getJustifyContent({ isStripe: true, totalTiles: 2, isLocalVideoAlone: false })).toBe('center')
+		})
+
+		test('keeps a lone local video at the end of the stripe', () => {
+			expect(getJustifyContent({ isStripe: true, totalTiles: 1, isLocalVideoAlone: true })).toBe('end')
+		})
+
+		test('keeps a lone remote tile at the start of the stripe', () => {
+			// The local video is not shown as a tile, so the only tile left is a
+			// remote one and it belongs to the start of the row
+			expect(getJustifyContent({ isStripe: true, totalTiles: 1, isLocalVideoAlone: false })).toBe('start')
+		})
+	})
 })
diff --git a/src/components/CallView/Grid/gridLayout.ts b/src/components/CallView/Grid/gridLayout.ts
index 7070d901026..5ebe4f05a60 100644
--- a/src/components/CallView/Grid/gridLayout.ts
+++ b/src/components/CallView/Grid/gridLayout.ts
@@ -375,3 +375,43 @@ export function computeTilePlacements({
 
 	return placements
 }
+
+/** Alignment of the tile columns within the grid */
+export type GridJustifyContent = 'center' | 'start' | 'end'
+
+type JustifyContentOptions = {
+	/** Whether the grid is shown as a stripe */
+	isStripe: boolean
+	/** Number of tiles laid out on the page, including the local video tile */
+	totalTiles: number
+	/** Whether the local video is the only tile of the grid */
+	isLocalVideoAlone: boolean
+}
+
+/**
+ * Alignment of the tile columns within the grid.
+ *
+ * The columns no longer take the whole width once they are capped, so the grid
+ * itself has to place them. They are centered, except in a stripe holding a
+ * single tile: that tile keeps the side it would sit on in a fuller stripe
+ * rather than moving to the middle. The local video is laid out after the
+ * remote ones, so it stays at the inline end, while a lone remote tile keeps
+ * the inline start the tiles are laid out from - which is where it belongs once
+ * the local video is not shown as a tile.
+ *
+ * @param options - the layout inputs
+ * @param options.isStripe - whether the grid is shown as a stripe
+ * @param options.totalTiles - number of tiles on the page, including the local video tile
+ * @param options.isLocalVideoAlone - whether the local video is the only tile
+ */
+export function getJustifyContent({
+	isStripe,
+	totalTiles,
+	isLocalVideoAlone,
+}: JustifyContentOptions): GridJustifyContent {
+	if (!isStripe || totalTiles !== 1) {
+		return 'center'
+	}
+
+	return isLocalVideoAlone ? 'end' : 'start'
+}
diff --git a/src/components/CallView/Grid/useGridDimensions.ts b/src/components/CallView/Grid/useGridDimensions.ts
index 953a92d2ec9..8af81439331 100644
--- a/src/components/CallView/Grid/useGridDimensions.ts
+++ b/src/components/CallView/Grid/useGridDimensions.ts
@@ -90,8 +90,21 @@ export function useGridDimensions({
 			return
 		}
 
-		gridWidth.value = element.clientWidth
-		gridHeight.value = element.clientHeight
+		const width = element.clientWidth
+		const height = element.clientHeight
+
+		// The grid is hidden or mid-transition (the stripe collapses and expands
+		// by its height): measuring it now would shrink the layout down to a
+		// single row and it would be kept until the next resize, as the element
+		// is given back its size by a transition rather than by a layout change
+		// of its own. Keep the current layout instead and wait for the
+		// `ResizeObserver` to report the final size.
+		if (width <= 0 || height <= 0) {
+			return
+		}
+
+		gridWidth.value = width
+		gridHeight.value = height
 
 		const dimensions = computeGridDimensions({
 			gridWidth: gridWidth.value,
@@ -115,10 +128,26 @@ export function useGridDimensions({
 	let resizeObserver: ResizeObserver | null = null
 
 	onMounted(() => {
+		resizeObserver = new ResizeObserver(debouncedRecompute)
+
 		if (wrapper.value) {
-			resizeObserver = new ResizeObserver(debouncedRecompute)
 			resizeObserver.observe(wrapper.value)
 		}
+
+		// The grid element is observed as well: it is the one being measured and
+		// its size does not always follow the size of the wrapper, which keeps
+		// the whole height of the call view while the grid is collapsed and
+		// expanded by a transition. The element is unmounted along with the
+		// collapsed stripe, so it is observed again whenever it comes back.
+		watch(grid, (element, previousElement) => {
+			if (previousElement) {
+				resizeObserver?.unobserve(previousElement)
+			}
+			if (element) {
+				resizeObserver?.observe(element)
+			}
+		}, { immediate: true })
+
 		recompute()
 	})
 
diff --git a/src/components/CallView/shared/VideoBackground.vue b/src/components/CallView/shared/VideoBackground.vue
index a3105f63158..0e3cee8c32e 100644
--- a/src/components/CallView/shared/VideoBackground.vue
+++ b/src/components/CallView/shared/VideoBackground.vue
@@ -21,12 +21,14 @@ const isDarkTheme = useIsDarkTheme()
 	top: 0;
 	height: 100%;
 	width: 100%;
-	background-color: rgba(var(--overlay-color), 0.3);
-	background-image: none;
+	// A solid surface: nothing of the call view behind the tile shows through
+	// it. The two colours are what the translucent tint they replace used to
+	// composite to over the background of the call, so a tile keeps the shade
+	// it had in either theme.
+	background-color: #363636;
 
-	--overlay-color: 0, 0, 0;
 	&.dark-theme {
-		--overlay-color: 255, 255, 255;
+		background-color: #515151;
 	}
 }
 </style>
diff --git a/src/components/CallView/shared/VideoVue.vue b/src/components/CallView/shared/VideoVue.vue
index 75d18ca2006..0ae1711138b 100644
--- a/src/components/CallView/shared/VideoVue.vue
+++ b/src/components/CallView/shared/VideoVue.vue
@@ -189,8 +189,9 @@ export default {
 			default: false,
 		},
 
-		// True when this video component is used in one to one conversations
-		isOneToOne: {
+		// True when this video fills the whole call view, with the stripe
+		// floating over it
+		isFullPage: {
 			type: Boolean,
 			default: false,
 		},
@@ -323,7 +324,7 @@ export default {
 				presenter: this.isPresenterOverlay && this.mouseover,
 				'video-container-grid': this.isGrid,
 				'video-container-big': this.isBig,
-				'one-to-one': this.isOneToOne,
+				'full-page': this.isFullPage,
 				'presenter-overlay': this.isPresenterOverlay,
 			}
 		},
@@ -654,7 +655,7 @@ export default {
 .video-container-big {
 	position: absolute;
 
-	&.one-to-one {
+	&.full-page {
 		width: calc(100% - var(--wrapper-padding) * 2);
 	}