diff --git a/packages/core/src/time.ts b/packages/core/src/time.ts
index a8db48a..6ffde07 100644
--- a/packages/core/src/time.ts
+++ b/packages/core/src/time.ts
@@ -86,6 +86,9 @@ export function nextBucket(bucket: number, granularity: Granularity, timeZone =
   }
 }
 
+/** Most buckets {@link bucketsBetween} returns before it throws. */
+export const MAX_BUCKETS = 10_000;
+
 /** Bucket starts covering the half-open interval [from, to). */
 export function bucketsBetween(
   from: number,
@@ -100,7 +103,8 @@ export function bucketsBetween(
     b = nextBucket(b, granularity, timeZone)
   ) {
     out.push(b);
-    if (out.length > 10_000) throw new RangeError('Range too large for the chosen granularity');
+    if (out.length > MAX_BUCKETS)
+      throw new RangeError('Range too large for the chosen granularity');
   }
   return out;
 }
diff --git a/server/src/routes/schemas.ts b/server/src/routes/schemas.ts
index be68360..6dcae50 100644
--- a/server/src/routes/schemas.ts
+++ b/server/src/routes/schemas.ts
@@ -1,4 +1,12 @@
-import { DAY, DIMENSIONS, type Dimension, type Granularity } from '@pulse/core';
+import {
+  DAY,
+  DIMENSIONS,
+  HOUR,
+  MAX_BUCKETS,
+  MINUTE,
+  type Dimension,
+  type Granularity,
+} from '@pulse/core';
 
 export const rangeQuerySchema = {
   type: 'object',
@@ -61,3 +69,17 @@ export function resolveRange(q: RangeQuerystring, now: number): { from: number;
   if (from >= to) return { from: to - DAY, to };
   return { from: Math.max(from, to - 400 * DAY), to };
 }
+
+const BUCKET_MS: Record<Granularity, number> = { minute: MINUTE, hour: HOUR, day: DAY };
+
+/**
+ * Longest range, in buckets, that a forced `interval` may cover. One less than
+ * MAX_BUCKETS because `from` snaps down to a bucket start, so a range n buckets
+ * long can touch n + 1 of them. With the 400-day clamp above, only `minute` can
+ * hit it.
+ */
+export const MAX_INTERVAL_SPAN = MAX_BUCKETS - 1;
+
+export function fitsInterval(range: { from: number; to: number }, interval: Granularity): boolean {
+  return range.to - range.from <= MAX_INTERVAL_SPAN * BUCKET_MS[interval];
+}
diff --git a/server/src/routes/stats.ts b/server/src/routes/stats.ts
index 6a58a7b..d050db4 100644
--- a/server/src/routes/stats.ts
+++ b/server/src/routes/stats.ts
@@ -2,7 +2,9 @@ import type { FastifyInstance, FastifyReply } from 'fastify';
 import type { AppContext } from '../context.js';
 import { toCsv } from '../stats/csv.js';
 import {
+  MAX_INTERVAL_SPAN,
   breakdownQuerySchema,
+  fitsInterval,
   rangeQuerySchema,
   resolveRange,
   siteParamsSchema,
@@ -38,11 +40,14 @@ export function statsRoutes(app: FastifyInstance, ctx: AppContext): void {
     { schema: { params: siteParamsSchema, querystring: timeseriesQuerySchema } },
     async (req, reply) => {
       if (!ensureSite(req.params.siteId, reply)) return reply;
-      return stats.timeseries(
-        req.params.siteId,
-        resolveRange(req.query, ctx.now()),
-        req.query.interval,
-      );
+      const range = resolveRange(req.query, ctx.now());
+      const { interval } = req.query;
+      if (interval && !fitsInterval(range, interval)) {
+        return reply.code(400).send({
+          error: `interval=${interval} covers at most ${MAX_INTERVAL_SPAN} ${interval}s; use a shorter range or a coarser interval`,
+        });
+      }
+      return stats.timeseries(req.params.siteId, range, interval);
     },
   );
 
diff --git a/server/test/api.test.ts b/server/test/api.test.ts
index 1ea26e2..a0b01b9 100644
--- a/server/test/api.test.ts
+++ b/server/test/api.test.ts
@@ -1,6 +1,8 @@
 import {
+  DAY,
   HOUR,
   MINUTE,
+  SECOND,
   type BreakdownResponse,
   type RealtimeResponse,
   type SummaryResponse,
@@ -113,6 +115,23 @@ describe('stats API', () => {
     );
   });
 
+  it('answers 400 when a forced interval needs too many buckets', async () => {
+    const minute = (from: number, to: number) =>
+      t.app.inject(`/api/sites/demo/timeseries?from=${from}&to=${to}&interval=minute`);
+    // The ranges from issue #1: 6 days worked, 8 days answered 500.
+    expect((await minute(NOW - 6 * DAY, NOW)).statusCode).toBe(200);
+    const tooLong = await minute(NOW - 8 * DAY, NOW);
+    expect(tooLong.statusCode).toBe(400);
+    expect(tooLong.json()).toEqual({ error: expect.stringContaining('interval=minute') });
+    // Exact boundary. `from` is off the minute grid and `to` is past now, so the
+    // series gets an extra partial bucket at the front and nothing is trimmed at the end.
+    const to = NOW + 30 * SECOND;
+    const longest = await minute(to - 9_999 * MINUTE, to);
+    expect(longest.statusCode).toBe(200);
+    expect(longest.json<TimeseriesResponse>().points).toHaveLength(10_000);
+    expect((await minute(to - 10_000 * MINUTE, to)).statusCode).toBe(400);
+  });
+
   it('breaks down by page, referrer, country and device', async () => {
     const range = `from=${NOW - 24 * HOUR}&to=${NOW + MINUTE}`;
     const pages = (