diff --git a/component/ElementCall.module.css b/component/ElementCall.module.css
index 461ad9b0c..f99dccb16 100644
--- a/component/ElementCall.module.css
+++ b/component/ElementCall.module.css
@@ -6,15 +6,26 @@ Please see LICENSE in the repository root for full details.
 */
 
 /* The container a host mounts us into. It fills whatever space the host gives
-it, and establishes a stacking context of its own so that our overlays and
-modals cannot escape it — which is the whole reason for embedding rather than
-using an iframe. */
+it, and nothing we draw may leave it.
+
+That takes two separate things, which are easy to mistake for one. `isolation`
+gives us a stacking context, so nothing inside can be layered above the host's
+own interface. Containment makes us the containing block for `position: fixed`
+descendants, and clips what we paint to our own box: without it, the modal
+scrim and dialog — which are positioned `fixed` and centred, since in the app
+they are meant to cover the page — resolve against the viewport and appear in
+the middle of the host's window rather than in the middle of the call.
+
+The clipping cuts both ways: a menu near the edge of a small container is
+trimmed rather than overflowing into the host. That is the trade being an
+embedded component makes. */
 .root {
   display: flex;
   flex-direction: column;
   inline-size: 100%;
   block-size: 100%;
   isolation: isolate;
+  contain: layout paint;
   position: relative;
   background-color: var(--cpd-color-bg-canvas-default);
   color: var(--cpd-color-text-primary);
diff --git a/src/button/ReactionToggleButton.module.css b/src/button/ReactionToggleButton.module.css
index 90c6af021..705d4d9ed 100644
--- a/src/button/ReactionToggleButton.module.css
+++ b/src/button/ReactionToggleButton.module.css
@@ -19,7 +19,12 @@
 }
 
 div.reactionPopupMenuRoot.reactionPopupMenuModal {
-  --overlay-top: 82vh;
+  /* Down near the footer it belongs to, rather than centred like other modals.
+  A percentage, not a viewport unit: the overlay is positioned `fixed`, so this
+  resolves against the page in the standalone app and against the container
+  when a host embeds us — where 82vh would put it below the container
+  entirely. */
+  --overlay-top: 82%;
   width: fit-content;
 }
 
diff --git a/src/room/ReactionsOverlay.module.css b/src/room/ReactionsOverlay.module.css
index 3738dc09e..618adbf38 100644
--- a/src/room/ReactionsOverlay.module.css
+++ b/src/room/ReactionsOverlay.module.css
@@ -3,8 +3,11 @@
   display: inline;
   z-index: 2;
   pointer-events: none;
-  width: 100vw;
-  height: 100vh;
+  /* Percentages, not viewport units: the containing block is the element
+  Element Call treats as its root, which is the page in the standalone app but
+  the container a host gave us when embedded. */
+  width: 100%;
+  height: 100%;
   left: 0;
   top: 0;
 }
@@ -16,7 +19,7 @@
   animation-name: reaction-up;
   width: fit-content;
   position: relative;
-  top: 80vh;
+  top: 80%;
 }
 
 @keyframes reaction-up {
@@ -24,7 +27,7 @@
     opacity: 1;
     translate: 0 0;
     scale: 200%;
-    top: 80vh;
+    top: 80%;
   }
 
   to {
@@ -48,7 +51,7 @@
   .reaction {
     font-size: 48pt;
     animation-name: reaction-up-reduced;
-    top: calc(-50vh + (48pt / 2));
-    left: calc(50vw - (48pt / 2)) !important;
+    top: calc(-50% + (48pt / 2));
+    left: calc(50% - (48pt / 2)) !important;
   }
 }