diff --git a/src/App.css b/src/App.css
index b9b949d5..056038df 100644
--- a/src/App.css
+++ b/src/App.css
@@ -2778,10 +2778,102 @@ body.has-player .chat-fab {
   padding: 0.35rem 0.85rem;
 }
 
+/* Amplitude of the header button's idle rocking, as a 0–1 scale. Registered
+   so it can be transitioned: the keyframes below multiply their offsets by it,
+   which turns a hard switch between still and rocking into a fade. */
+@property --btn-bob {
+  syntax: "<number>";
+  inherits: false;
+  initial-value: 0;
+}
+
 .app-header-nav .btn-primary {
   padding: 0.35rem 1rem;
 }
 
+/* `:not(:disabled)` earns this rule a third class's worth of weight, which it
+   needs: geocities and brutalist re-declare the whole `transition` shorthand
+   on every button at one class plus one element plus a :not, and neither list
+   mentions `translate`, so without it their lists win and the lift lands
+   instantly instead of easing. Nothing here applies to a disabled button
+   anyway — it can't be hovered. */
+.app-header-nav .btn-primary:not(:disabled) {
+  /* Pivot at the bottom edge, so the rock below reads as a head on a neck
+     rather than as the whole button spinning about its middle. */
+  transform-origin: 50% 100%;
+  /* Both motions are declared here rather than on :hover, and held paused, so
+     that leaving the button fades the rocking out instead of cutting it: the
+     amplitude eases to zero under an animation that is merely frozen. Paused
+     also means an untouched button isn't animating a thing. */
+  animation:
+    btn-hover-tilt 2.6s ease-in-out infinite,
+    btn-hover-float 3.4s ease-in-out infinite;
+  animation-play-state: paused;
+  /* The lift is carried by `translate` rather than `transform` so the rocking,
+     which needs `transform` and `rotate` to itself, composes with it instead
+     of replacing it. It eases in and out rather than out alone — a fast start
+     is what made the button feel like it snapped up to meet the cursor. */
+  transition:
+    background var(--dur-base),
+    color var(--dur-base),
+    border-color var(--dur-base),
+    box-shadow var(--dur-base),
+    translate var(--dur-lift) var(--ease-in-out),
+    --btn-bob var(--dur-bob-fade) var(--ease-in-out);
+}
+
+.app-header-nav .btn-primary:hover:not(:disabled) {
+  translate: 0 -2px;
+  /* The rocking starts the moment the lift does, but from nothing, and takes
+     longer than the lift to reach full throw — so the button is already
+     drifting as it settles, and never visibly changes gear. */
+  --btn-bob: 1;
+  animation-play-state: running;
+}
+
+/* Pressing puts it back down flat — the base :active transform can only take
+   effect once the animation stops claiming `transform`. */
+.app-header-nav .btn-primary:active:not(:disabled) {
+  translate: none;
+  animation: none;
+  --btn-bob: 0;
+  /* The press has to land at once — at the lift's own easing it would float
+     back down under the finger. */
+  transition-duration: var(--dur-fast);
+}
+
+/* The rock is the motion; the float underneath it is small and on a period
+   that doesn't divide the rock's, so the two never line up the same way twice
+   and it never settles into a metronome. */
+@keyframes btn-hover-tilt {
+  0%,
+  100% {
+    rotate: 0deg;
+  }
+  25% {
+    rotate: calc(var(--btn-bob, 0) * 2.5deg);
+  }
+  75% {
+    rotate: calc(var(--btn-bob, 0) * -2.5deg);
+  }
+}
+
+@keyframes btn-hover-float {
+  0%,
+  100% {
+    transform: translateY(0);
+  }
+  50% {
+    transform: translateY(calc(var(--btn-bob, 0) * -2px));
+  }
+}
+
+@media (prefers-reduced-motion: reduce) {
+  .app-header-nav .btn-primary {
+    animation: none;
+  }
+}
+
 /* Icon-only controls are square, so the row reads as a tidy set. */
 .app-header-nav .nav-search-btn,
 .app-header-nav .notification-bell,
diff --git a/src/themes/brutalist.css b/src/themes/brutalist.css
index 59067524..89bb8b14 100644
--- a/src/themes/brutalist.css
+++ b/src/themes/brutalist.css
@@ -364,6 +364,13 @@
   transform: translate(2px, 2px);
 }
 
+/* The header's dump button floats in the base theme; here it presses into the
+   page instead, so neither the lift nor the idle drift applies. */
+[data-style="brutalist"] .app-header-nav .btn-primary:hover:not(:disabled) {
+  translate: none;
+  animation: none;
+}
+
 /* ── btn-border ──────────────────────────────────────────────────── */
 [data-style="brutalist"] .btn-border {
   box-shadow: 2px 2px 0 var(--color-border);
diff --git a/src/themes/nyt.css b/src/themes/nyt.css
index 926703c4..8b7e2743 100644
--- a/src/themes/nyt.css
+++ b/src/themes/nyt.css
@@ -356,6 +356,12 @@
   transform: none;
 }
 
+/* Flat ink on paper: the header's dump button doesn't lift or drift either. */
+[data-style="nyt"] .app-header-nav .btn-primary:hover:not(:disabled) {
+  translate: none;
+  animation: none;
+}
+
 /* Secondary / outline buttons — plain hairline box */
 
 /* ── Inputs — clean field, ink focus ─────────────────────────────── */
diff --git a/src/tokens.css b/src/tokens.css
index be0ffce9..00f2c8f0 100644
--- a/src/tokens.css
+++ b/src/tokens.css
@@ -86,6 +86,10 @@
   --dur-base: 0.15s;
   --dur-slow: 0.2s;
   --dur-reveal: 0.25s;
+  /* A hover lift long enough not to snap, and the slower fade that brings the
+     idle rocking in over the top of it. */
+  --dur-lift: 0.4s;
+  --dur-bob-fade: 0.9s;
 
   /* ── Layers ── */
   --z-raised: 1;