diff --git a/lib/sponsors.ts b/lib/sponsors.ts
index e4c96c954..7c14a5fcd 100644
--- a/lib/sponsors.ts
+++ b/lib/sponsors.ts
@@ -107,8 +107,9 @@ export function makeIconSets(
         const toPick = icons.map(icon => {
             return {
                 icon: icon,
-                // Number of times we'd expect to see this, divided by number of times we saw it
-                error: result.length / icon.topIconShowEvery / (sponsorAppearanceCount.get(icon) || 0.00001),
+                // Number of times we'd expect to see this, divided by number of times we saw it, assuming that we pick
+                // this one next.
+                error: (result.length + 1) / icon.topIconShowEvery / ((sponsorAppearanceCount.get(icon) || 0) + 1),
             };
         });
         toPick.sort((lhs, rhs) => rhs.error - lhs.error);
diff --git a/test/sponsors-test.ts b/test/sponsors-test.ts
index 8b1236f82..f878b241e 100644
--- a/test/sponsors-test.ts
+++ b/test/sponsors-test.ts
@@ -226,6 +226,23 @@ levels:
         ]);
         expect(() => makeIconSets(icons, 2)).toThrow();
     });
+    it('should pick icons appropriately when one is required every time and the others fit in ok every 3', () => {
+        const sponsor1 = parse({name: 'Sponsor1', topIconShowEvery: 1, icon: '1'});
+        const sponsor2 = parse({name: 'Sponsor2', topIconShowEvery: 3, icon: '2'});
+        const sponsor3 = parse({name: 'Sponsor3', topIconShowEvery: 3, icon: '3'});
+        const sponsor4 = parse({name: 'Sponsor4', topIconShowEvery: 3, icon: '4'});
+        const sponsor5 = parse({name: 'Sponsor5', topIconShowEvery: 3, icon: '5'});
+        const sponsor6 = parse({name: 'Sponsor6', topIconShowEvery: 3, icon: '6'});
+        const icons = [sponsor1, sponsor2, sponsor3, sponsor4, sponsor5, sponsor6];
+        expect(makeIconSets(icons, 10)).toEqual([icons]);
+        expect(makeIconSets(icons, 3)).toEqual([
+            [sponsor1, sponsor2, sponsor3],
+            [sponsor1, sponsor4, sponsor5],
+            [sponsor1, sponsor2, sponsor6],
+            [sponsor1, sponsor3, sponsor4],
+            [sponsor1, sponsor5, sponsor6],
+        ]);
+    });
 });
 
 describe('Our specific sponsor file', () => {