diff --git a/h3.c b/h3.c
index 5c921763..e2619587 100644
--- a/h3.c
+++ b/h3.c
@@ -510,7 +510,8 @@ static int h3_valid_params(h3_ctx *ctx, const h3_params *params) {
             return 0;
         }
     }
-    if (params->frames < 5 || h3_align_frame_count(params->frames) > 362) {
+    int aligned_frames = h3_align_frame_count(params->frames);
+    if (params->frames < 5 || !aligned_frames || aligned_frames > 362) {
         h3_set_error(ctx, "frames must align within the released 5..362 range");
         return 0;
     }
diff --git a/h3_host.c b/h3_host.c
index a04a2a0a..94d0409e 100644
--- a/h3_host.c
+++ b/h3_host.c
@@ -13,11 +13,11 @@ static const int h3_frame_per_token[5] = {1, 4, 4, 4, 4};
 static const double h3_frame_rescale = 5.0 / 3.0;
 
 int h3_align_frame_count(int requested) {
-    int value = requested < 5 ? 5 : requested;
-    int remainder = (value - 5) % 17;
+    int64_t value = requested < 5 ? 5 : requested;
+    int64_t remainder = (value - 5) % 17;
     if (remainder < 0) remainder += 17;
     if (remainder != 0) value += 17 - remainder;
-    return value;
+    return value > INT_MAX ? 0 : (int)value;
 }
 
 int h3_video_latent_t(int frame_count) {
diff --git a/h3_host.h b/h3_host.h
index f71eded7..3fbfe4a7 100644
--- a/h3_host.h
+++ b/h3_host.h
@@ -92,6 +92,7 @@ typedef struct {
     int has_spare;
 } h3_rng;
 
+/* Return the next legal frame count, or zero if it cannot fit in an int. */
 int h3_align_frame_count(int requested);
 int h3_video_latent_t(int frame_count);
 int h3_video_encoder_latent_t(int frame_count);
diff --git a/tests/test_h3.c b/tests/test_h3.c
index 3f66fa32..69a50fb3 100644
--- a/tests/test_h3.c
+++ b/tests/test_h3.c
@@ -37,6 +37,7 @@ static void test_temporal_and_canvas(void) {
         CHECK(got.video_t == cases[index].video_t);
         CHECK(got.audio_t == cases[index].audio_t);
     }
+    CHECK(h3_align_frame_count(INT32_MAX) == 0);
     CHECK(h3_video_encoder_latent_t(1) == 1);
     CHECK(h3_video_encoder_latent_t(5) == 2);
     CHECK(h3_video_encoder_latent_t(22) == 6);