diff --git a/components/graph-coverage.tsx b/components/graph-coverage.tsx
index a21b5a9..e49e5b9 100644
--- a/components/graph-coverage.tsx
+++ b/components/graph-coverage.tsx
@@ -102,7 +102,7 @@ export function GraphCoverageControl({ refreshKey = 0 }: { refreshKey?: number }
 				title="Extraction coverage — what the knowledge graph has covered"
 				aria-expanded={open}
 				onClick={() => setOpen((o) => !o)}
-				className={`flex size-11 items-center justify-center rounded-xl border bg-card/85 shadow-lg backdrop-blur transition-colors hover:bg-accent ${
+				className={`flex size-9 items-center justify-center rounded-xl border bg-card/85 shadow-lg backdrop-blur transition-colors hover:bg-accent ${
 					open ? "text-foreground" : "text-muted-foreground hover:text-foreground"
 				}`}
 			>
diff --git a/components/graph-view.tsx b/components/graph-view.tsx
index 2aa6609..e75faa1 100644
--- a/components/graph-view.tsx
+++ b/components/graph-view.tsx
@@ -361,7 +361,7 @@ function GraphSettingsControl({
 				title="Rendering settings"
 				aria-expanded={open}
 				onClick={() => setOpen((o) => !o)}
-				className={`flex size-11 items-center justify-center rounded-xl border bg-card/85 shadow-lg backdrop-blur transition-colors hover:bg-accent ${
+				className={`flex size-9 items-center justify-center rounded-xl border bg-card/85 shadow-lg backdrop-blur transition-colors hover:bg-accent ${
 					open ? "text-foreground" : "text-muted-foreground hover:text-foreground"
 				}`}
 			>
@@ -1134,24 +1134,35 @@ export function GraphView() {
 			    coverage, import, gear — coverage sits between search and
 			    import; the gear keeps the corner. items-start (not center)
 			    so the search container's no-match note can grow downward
-			    without shifting its siblings — every button is 44px tall,
-			    top alignment pins the row. Coverage renders even when the
-			    graph is EMPTY — an empty graph with unextracted sessions is
-			    exactly when it matters (extract → the graph gains nodes).
+			    without shifting its siblings — every control is 36px tall
+			    (header band, 2026-09-20), top alignment pins the row.
+			    Coverage renders even when the graph is EMPTY — an empty
+			    graph with unextracted sessions is exactly when it matters
+			    (extract → the graph gains nodes).
 			    lh-no-drag (2026-09-17): home.tsx's floating drag strip
 			    underlays this row — Electron's drag mask ignores z-index,
 			    so without an explicit carve-out the controls were
-			    unclickable in the desktop app (owner report). max-w + flex-wrap
-			    (narrow-window wave, 2026-09-17): below the sidebar auto-close
-			    threshold the row wraps to a second line instead of overflowing
-			    left over the header toggle cluster (92px gutter + 36px button);
-			    9rem keeps one clear column of air alongside it. */}
-			<div className="lh-no-drag absolute right-3 top-3 z-10 flex flex-col items-end gap-2">
-			<div className="flex max-w-[calc(100%-9rem)] flex-wrap items-start gap-2">
+			    unclickable in the desktop app (owner report). The old
+			    flex-wrap (narrow-window wave, 2026-09-17) folded the row
+			    onto two lines below the sidebar threshold — owner rejected
+			    it (2026-09-20): one row always, the search shrinks (see
+			    the header-band comment on the column below). */}
+			{/* Header band (owner, 2026-09-20): the controls sit IN the
+			    header's visual row — top-2 aligns with the sidebar toggle's
+			    band (header py-2, toggle h-9), every control slimmed to 36px.
+			    The width cap lives HERE on the absolute element (100% resolves
+			    against the full-bleed parent) — the row NEVER wraps (owner
+			    rejected the two-row fold); in narrow windows the search is
+			    the flexible element and shrinks instead. */}
+			<div className="lh-no-drag absolute right-3 top-2 z-10 flex max-w-[calc(100%-5.5rem)] flex-col items-end gap-2">
+			<div className="flex min-w-0 items-start gap-2">
 				{!isEmpty && (
 					<>
-					{/* Search — its own container (icon + input + no-match note). */}
-					<div className="w-56 rounded-xl border bg-card/85 p-1.5 shadow-lg backdrop-blur">
+					{/* Search — its own container (icon + input + no-match note).
+					    The header band's flexible element: w-56 normally, shrinks
+					    (min-w-0) when the column's width cap binds in narrow
+					    windows — the row's other controls are shrink-0. */}
+					<div className="w-56 min-w-0 shrink rounded-xl border bg-card/85 px-1 py-[3px] shadow-lg backdrop-blur">
 						<div className="relative">
 							<SearchIcon className="absolute left-2.5 top-1/2 size-3.5 -translate-y-1/2 text-muted-foreground" />
 							<input
@@ -1160,7 +1171,7 @@ export function GraphView() {
 								onChange={(e) => setQuery(e.target.value)}
 								placeholder="Search nodes…"
 								spellCheck={false}
-								className="h-8 w-full rounded-lg border bg-background pl-8 text-xs outline-none placeholder:text-muted-foreground focus:border-ring"
+								className="h-7 w-full rounded-lg border bg-background pl-8 text-xs outline-none placeholder:text-muted-foreground focus:border-ring"
 							/>
 						</div>
 						{snapshot !== null && visibleIds.size === 0 && query.trim() !== "" && (
@@ -1176,11 +1187,11 @@ export function GraphView() {
 					with unextracted sessions is exactly when it matters (extract
 					→ the graph gains nodes). The panel re-reads when background
 					runs settle (refreshTick). */}
-				<GraphCoverageControl refreshKey={refreshTick} />
+				<div className="shrink-0"><GraphCoverageControl refreshKey={refreshTick} /></div>
 				{!isEmpty && (
 				<>
-					{/* Import notes — its own container. */}
-					<div className="rounded-xl border bg-card/85 p-1.5 shadow-lg backdrop-blur">
+					{/* Import notes — its own container (36px, header band). */}
+					<div className="shrink-0 rounded-xl border bg-card/85 px-1 py-[3px] shadow-lg backdrop-blur">
 						<input
 							ref={fileInputRef}
 							type="file"
@@ -1196,7 +1207,7 @@ export function GraphView() {
 							type="button"
 							disabled={importing}
 							onClick={() => fileInputRef.current?.click()}
-							className="flex h-8 items-center gap-1.5 rounded-lg px-3 text-xs text-muted-foreground transition-colors hover:bg-accent disabled:opacity-50"
+							className="flex h-7 items-center gap-1.5 rounded-lg px-2.5 text-xs text-muted-foreground transition-colors hover:bg-accent disabled:opacity-50"
 						>
 							<UploadIcon className="size-3" />
 							{importing ? "Importing…" : "Import notes…"}