diff --git a/src/secp256k1/include/secp256k1.h b/src/secp256k1/include/secp256k1.h
--- a/src/secp256k1/include/secp256k1.h
+++ b/src/secp256k1/include/secp256k1.h
@@ -260,12 +260,10 @@
  *
  *  Returns: a newly created scratch space.
  *  Args: ctx:  an existing context object (cannot be NULL)
- *  In:  init_size: initial amount of memory to allocate
- *        max_size: maximum amount of memory to allocate
+ *  In:   max_size: maximum amount of memory to allocate
  */
 SECP256K1_API SECP256K1_WARN_UNUSED_RESULT secp256k1_scratch_space* secp256k1_scratch_space_create(
     const secp256k1_context* ctx,
-    size_t init_size,
     size_t max_size
 ) SECP256K1_ARG_NONNULL(1);
 
diff --git a/src/secp256k1/src/bench_ecmult.c b/src/secp256k1/src/bench_ecmult.c
--- a/src/secp256k1/src/bench_ecmult.c
+++ b/src/secp256k1/src/bench_ecmult.c
@@ -154,7 +154,7 @@
     /* Allocate stuff */
     data.ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
     scratch_size = secp256k1_strauss_scratch_size(POINTS) + STRAUSS_SCRATCH_OBJECTS*16;
-    data.scratch = secp256k1_scratch_space_create(data.ctx, scratch_size, scratch_size);
+    data.scratch = secp256k1_scratch_space_create(data.ctx, scratch_size);
     data.scalars = malloc(sizeof(secp256k1_scalar) * POINTS);
     data.seckeys = malloc(sizeof(secp256k1_scalar) * POINTS);
     data.pubkeys = malloc(sizeof(secp256k1_ge) * POINTS);
diff --git a/src/secp256k1/src/ecmult_impl.h b/src/secp256k1/src/ecmult_impl.h
--- a/src/secp256k1/src/ecmult_impl.h
+++ b/src/secp256k1/src/ecmult_impl.h
@@ -525,10 +525,9 @@
         return 1;
     }
 
-    if (!secp256k1_scratch_resize(scratch, secp256k1_strauss_scratch_size(n_points), STRAUSS_SCRATCH_OBJECTS)) {
+    if (!secp256k1_scratch_allocate_frame(scratch, secp256k1_strauss_scratch_size(n_points), STRAUSS_SCRATCH_OBJECTS)) {
         return 0;
     }
-    secp256k1_scratch_reset(scratch);
     points = (secp256k1_gej*)secp256k1_scratch_alloc(scratch, n_points * sizeof(secp256k1_gej));
     scalars = (secp256k1_scalar*)secp256k1_scratch_alloc(scratch, n_points * sizeof(secp256k1_scalar));
     state.prej = (secp256k1_gej*)secp256k1_scratch_alloc(scratch, n_points * ECMULT_TABLE_SIZE(WINDOW_A) * sizeof(secp256k1_gej));
@@ -543,10 +542,14 @@
 
     for (i = 0; i < n_points; i++) {
         secp256k1_ge point;
-        if (!cb(&scalars[i], &point, i+cb_offset, cbdata)) return 0;
+        if (!cb(&scalars[i], &point, i+cb_offset, cbdata)) {
+            secp256k1_scratch_deallocate_frame(scratch);
+            return 0;
+        }
         secp256k1_gej_set_ge(&points[i], &point);
     }
     secp256k1_ecmult_strauss_wnaf(ctx, &state, r, n_points, points, scalars, inp_g_sc);
+    secp256k1_scratch_deallocate_frame(scratch);
     return 1;
 }
 
@@ -873,10 +876,9 @@
     }
 
     bucket_window = secp256k1_pippenger_bucket_window(n_points);
-    if (!secp256k1_scratch_resize(scratch, secp256k1_pippenger_scratch_size(n_points, bucket_window), PIPPENGER_SCRATCH_OBJECTS)) {
+    if (!secp256k1_scratch_allocate_frame(scratch, secp256k1_pippenger_scratch_size(n_points, bucket_window), PIPPENGER_SCRATCH_OBJECTS)) {
         return 0;
     }
-    secp256k1_scratch_reset(scratch);
     points = (secp256k1_ge *) secp256k1_scratch_alloc(scratch, entries * sizeof(*points));
     scalars = (secp256k1_scalar *) secp256k1_scratch_alloc(scratch, entries * sizeof(*scalars));
     state_space = (struct secp256k1_pippenger_state *) secp256k1_scratch_alloc(scratch, sizeof(*state_space));
@@ -896,6 +898,7 @@
 
     while (point_idx < n_points) {
         if (!cb(&scalars[idx], &points[idx], point_idx + cb_offset, cbdata)) {
+            secp256k1_scratch_deallocate_frame(scratch);
             return 0;
         }
         idx++;
@@ -919,6 +922,7 @@
     for(i = 0; i < 1<<bucket_window; i++) {
         secp256k1_gej_clear(&buckets[i]);
     }
+    secp256k1_scratch_deallocate_frame(scratch);
     return 1;
 }
 
diff --git a/src/secp256k1/src/scratch.h b/src/secp256k1/src/scratch.h
--- a/src/secp256k1/src/scratch.h
+++ b/src/secp256k1/src/scratch.h
@@ -7,29 +7,33 @@
 #ifndef _SECP256K1_SCRATCH_
 #define _SECP256K1_SCRATCH_
 
+#define SECP256K1_SCRATCH_MAX_FRAMES	5
+
 /* The typedef is used internally; the struct name is used in the public API
  * (where it is exposed as a different typedef) */
 typedef struct secp256k1_scratch_space_struct {
-    void *data;
-    size_t offset;
-    size_t init_size;
+    void *data[SECP256K1_SCRATCH_MAX_FRAMES];
+    size_t offset[SECP256K1_SCRATCH_MAX_FRAMES];
+    size_t frame_size[SECP256K1_SCRATCH_MAX_FRAMES];
+    size_t frame;
     size_t max_size;
     const secp256k1_callback* error_callback;
 } secp256k1_scratch;
 
-static secp256k1_scratch* secp256k1_scratch_create(const secp256k1_callback* error_callback, size_t init_size, size_t max_size);
+static secp256k1_scratch* secp256k1_scratch_create(const secp256k1_callback* error_callback, size_t max_size);
+
 static void secp256k1_scratch_destroy(secp256k1_scratch* scratch);
 
+/** Attempts to allocate a new stack frame with `n` available bytes. Returns 1 on success, 0 on failure */
+static int secp256k1_scratch_allocate_frame(secp256k1_scratch* scratch, size_t n, size_t objects);
+
+/** Deallocates a stack frame */
+static void secp256k1_scratch_deallocate_frame(secp256k1_scratch* scratch);
+
 /** Returns the maximum allocation the scratch space will allow */
 static size_t secp256k1_scratch_max_allocation(const secp256k1_scratch* scratch, size_t n_objects);
 
-/** Attempts to allocate so that there are `n` available bytes. Returns 1 on success, 0 on failure */
-static int secp256k1_scratch_resize(secp256k1_scratch* scratch, size_t n, size_t n_objects);
-
-/** Returns a pointer into the scratch space or NULL if there is insufficient available space */
+/** Returns a pointer into the most recently allocated frame, or NULL if there is insufficient available space */
 static void *secp256k1_scratch_alloc(secp256k1_scratch* scratch, size_t n);
 
-/** Resets the returned pointer to the beginning of space */
-static void secp256k1_scratch_reset(secp256k1_scratch* scratch);
-
 #endif
diff --git a/src/secp256k1/src/scratch_impl.h b/src/secp256k1/src/scratch_impl.h
--- a/src/secp256k1/src/scratch_impl.h
+++ b/src/secp256k1/src/scratch_impl.h
@@ -15,16 +15,10 @@
  * TODO: Determine this at configure time. */
 #define ALIGNMENT 16
 
-static secp256k1_scratch* secp256k1_scratch_create(const secp256k1_callback* error_callback, size_t init_size, size_t max_size) {
+static secp256k1_scratch* secp256k1_scratch_create(const secp256k1_callback* error_callback, size_t max_size) {
     secp256k1_scratch* ret = (secp256k1_scratch*)checked_malloc(error_callback, sizeof(*ret));
     if (ret != NULL) {
-        ret->data = checked_malloc(error_callback, init_size);
-        if (ret->data == NULL) {
-            free (ret);
-            return NULL;
-        }
-        ret->offset = 0;
-        ret->init_size = init_size;
+        memset(ret, 0, sizeof(*ret));
         ret->max_size = max_size;
         ret->error_callback = error_callback;
     }
@@ -33,45 +27,60 @@
 
 static void secp256k1_scratch_destroy(secp256k1_scratch* scratch) {
     if (scratch != NULL) {
-        free(scratch->data);
+        VERIFY_CHECK(scratch->frame == 0);
         free(scratch);
     }
 }
 
 static size_t secp256k1_scratch_max_allocation(const secp256k1_scratch* scratch, size_t objects) {
-    if (scratch->max_size <= objects * ALIGNMENT) {
+    size_t i = 0;
+    size_t allocated = 0;
+    for (i = 0; i < scratch->frame; i++) {
+        allocated += scratch->frame_size[i];
+    }
+    if (scratch->max_size - allocated <= objects * ALIGNMENT) {
         return 0;
     }
-    return scratch->max_size - objects * ALIGNMENT;
+    return scratch->max_size - allocated - objects * ALIGNMENT;
 }
 
-static int secp256k1_scratch_resize(secp256k1_scratch* scratch, size_t n, size_t objects) {
-    n += objects * ALIGNMENT;
-    if (n > scratch->init_size && n <= scratch->max_size) {
-        void *tmp = checked_realloc(scratch->error_callback, scratch->data, n);
-        if (tmp == NULL) {
+static int secp256k1_scratch_allocate_frame(secp256k1_scratch* scratch, size_t n, size_t objects) {
+    VERIFY_CHECK(scratch->frame < SECP256K1_SCRATCH_MAX_FRAMES);
+
+    if (n <= secp256k1_scratch_max_allocation(scratch, objects)) {
+        n += objects * ALIGNMENT;
+        scratch->data[scratch->frame] = checked_malloc(scratch->error_callback, n);
+        if (scratch->data[scratch->frame] == NULL) {
             return 0;
         }
-        scratch->init_size = n;
-        scratch->data = tmp;
+        scratch->frame_size[scratch->frame] = n;
+        scratch->offset[scratch->frame] = 0;
+        scratch->frame++;
+        return 1;
+    } else {
+        return 0;
     }
-    return n <= scratch->max_size;
+}
+
+static void secp256k1_scratch_deallocate_frame(secp256k1_scratch* scratch) {
+    VERIFY_CHECK(scratch->frame > 0);
+    scratch->frame -= 1;
+    free(scratch->data[scratch->frame]);
 }
 
 static void *secp256k1_scratch_alloc(secp256k1_scratch* scratch, size_t size) {
     void *ret;
+    size_t frame = scratch->frame - 1;
     size = ((size + ALIGNMENT - 1) / ALIGNMENT) * ALIGNMENT;
-    if (size + scratch->offset > scratch->init_size) {
+
+    if (scratch->frame == 0 || size + scratch->offset[frame] > scratch->frame_size[frame]) {
         return NULL;
     }
-    ret = (void *) ((unsigned char *) scratch->data + scratch->offset);
+    ret = (void *) ((unsigned char *) scratch->data[frame] + scratch->offset[frame]);
     memset(ret, 0, size);
-    scratch->offset += size;
-    return ret;
-}
+    scratch->offset[frame] += size;
 
-static void secp256k1_scratch_reset(secp256k1_scratch* scratch) {
-    scratch->offset = 0;
+    return ret;
 }
 
 #endif
diff --git a/src/secp256k1/src/secp256k1.c b/src/secp256k1/src/secp256k1.c
--- a/src/secp256k1/src/secp256k1.c
+++ b/src/secp256k1/src/secp256k1.c
@@ -115,11 +115,9 @@
     ctx->error_callback.data = data;
 }
 
-secp256k1_scratch_space* secp256k1_scratch_space_create(const secp256k1_context* ctx, size_t init_size, size_t max_size) {
+secp256k1_scratch_space* secp256k1_scratch_space_create(const secp256k1_context* ctx, size_t max_size) {
     VERIFY_CHECK(ctx != NULL);
-    ARG_CHECK(max_size >= init_size);
-
-    return secp256k1_scratch_create(&ctx->error_callback, init_size, max_size);
+    return secp256k1_scratch_create(&ctx->error_callback, max_size);
 }
 
 void secp256k1_scratch_space_destroy(secp256k1_scratch_space* scratch) {
diff --git a/src/secp256k1/src/tests.c b/src/secp256k1/src/tests.c
--- a/src/secp256k1/src/tests.c
+++ b/src/secp256k1/src/tests.c
@@ -258,28 +258,31 @@
 
     /* Test public API */
     secp256k1_context_set_illegal_callback(none, counting_illegal_callback_fn, &ecount);
-    scratch = secp256k1_scratch_space_create(none, 100, 10);
-    CHECK(scratch == NULL);
-    CHECK(ecount == 1);
-
-    scratch = secp256k1_scratch_space_create(none, 100, 100);
-    CHECK(scratch != NULL);
-    CHECK(ecount == 1);
-    secp256k1_scratch_space_destroy(scratch);
 
-    scratch = secp256k1_scratch_space_create(none, 100, 1000);
+    scratch = secp256k1_scratch_space_create(none, 1000);
     CHECK(scratch != NULL);
-    CHECK(ecount == 1);
+    CHECK(ecount == 0);
 
     /* Test internal API */
     CHECK(secp256k1_scratch_max_allocation(scratch, 0) == 1000);
     CHECK(secp256k1_scratch_max_allocation(scratch, 1) < 1000);
-    CHECK(secp256k1_scratch_resize(scratch, 50, 1) == 1);  /* no-op */
-    CHECK(secp256k1_scratch_resize(scratch, 200, 1) == 1);
-    CHECK(secp256k1_scratch_resize(scratch, 950, 1) == 1);
-    CHECK(secp256k1_scratch_resize(scratch, 1000, 1) == 0);
-    CHECK(secp256k1_scratch_resize(scratch, 2000, 1) == 0);
+
+    /* Allocating 500 bytes with no frame fails */
+    CHECK(secp256k1_scratch_alloc(scratch, 500) == NULL);
+    CHECK(secp256k1_scratch_max_allocation(scratch, 0) == 1000);
+
+    /* ...but pushing a new stack frame does affect the max allocation */
+    CHECK(secp256k1_scratch_allocate_frame(scratch, 500, 1) == 1);
+    CHECK(secp256k1_scratch_max_allocation(scratch, 1) < 500); /* 500 - ALIGNMENT */
+    CHECK(secp256k1_scratch_alloc(scratch, 500) != NULL);
+    CHECK(secp256k1_scratch_alloc(scratch, 500) == NULL);
+
+    CHECK(secp256k1_scratch_allocate_frame(scratch, 500, 1) == 0);
+
+    /* ...and this effect is undone by popping the frame */
+    secp256k1_scratch_deallocate_frame(scratch);
     CHECK(secp256k1_scratch_max_allocation(scratch, 0) == 1000);
+    CHECK(secp256k1_scratch_alloc(scratch, 500) == NULL);
 
     /* cleanup */
     secp256k1_scratch_space_destroy(scratch);
@@ -2558,7 +2561,6 @@
     data.sc = sc;
     data.pt = pt;
     secp256k1_scalar_set_int(&szero, 0);
-    secp256k1_scratch_reset(scratch);
 
     /* No points to multiply */
     CHECK(ecmult_multi(&ctx->ecmult_ctx, scratch, &r, NULL, ecmult_multi_callback, &data, 0));
@@ -2590,7 +2592,7 @@
         CHECK(secp256k1_gej_is_infinity(&r));
 
         /* Try to multiply 1 point, but scratch space is empty */
-        scratch_empty = secp256k1_scratch_create(&ctx->error_callback, 0, 0);
+        scratch_empty = secp256k1_scratch_create(&ctx->error_callback, 0);
         CHECK(!ecmult_multi(&ctx->ecmult_ctx, scratch_empty, &r, &szero, ecmult_multi_callback, &data, 1));
         secp256k1_scratch_destroy(scratch_empty);
 
@@ -2816,7 +2818,7 @@
     int bucket_window = 0;
 
     for(; scratch_size < max_size; scratch_size+=256) {
-        scratch = secp256k1_scratch_create(&ctx->error_callback, 0, scratch_size);
+        scratch = secp256k1_scratch_create(&ctx->error_callback, scratch_size);
         CHECK(scratch != NULL);
         n_points_supported = secp256k1_pippenger_max_points(scratch);
         if (n_points_supported == 0) {
@@ -2824,7 +2826,8 @@
             continue;
         }
         bucket_window = secp256k1_pippenger_bucket_window(n_points_supported);
-        CHECK(secp256k1_scratch_resize(scratch, secp256k1_pippenger_scratch_size(n_points_supported, bucket_window), PIPPENGER_SCRATCH_OBJECTS));
+        CHECK(secp256k1_scratch_allocate_frame(scratch, secp256k1_pippenger_scratch_size(n_points_supported, bucket_window), PIPPENGER_SCRATCH_OBJECTS));
+        secp256k1_scratch_deallocate_frame(scratch);
         secp256k1_scratch_destroy(scratch);
     }
     CHECK(bucket_window == PIPPENGER_MAX_BUCKET_WINDOW);
@@ -2866,13 +2869,13 @@
     data.pt = pt;
 
     /* Test with empty scratch space */
-    scratch = secp256k1_scratch_create(&ctx->error_callback, 0, 0);
+    scratch = secp256k1_scratch_create(&ctx->error_callback, 0);
     CHECK(!secp256k1_ecmult_multi_var(&ctx->ecmult_ctx, scratch, &r, &scG, ecmult_multi_callback, &data, 1));
     secp256k1_scratch_destroy(scratch);
 
     /* Test with space for 1 point in pippenger. That's not enough because
      * ecmult_multi selects strauss which requires more memory. */
-    scratch = secp256k1_scratch_create(&ctx->error_callback, 0, secp256k1_pippenger_scratch_size(1, 1) + PIPPENGER_SCRATCH_OBJECTS*ALIGNMENT);
+    scratch = secp256k1_scratch_create(&ctx->error_callback, secp256k1_pippenger_scratch_size(1, 1) + PIPPENGER_SCRATCH_OBJECTS*ALIGNMENT);
     CHECK(!secp256k1_ecmult_multi_var(&ctx->ecmult_ctx, scratch, &r, &scG, ecmult_multi_callback, &data, 1));
     secp256k1_scratch_destroy(scratch);
 
@@ -2881,10 +2884,10 @@
         if (i > ECMULT_PIPPENGER_THRESHOLD) {
             int bucket_window = secp256k1_pippenger_bucket_window(i);
             size_t scratch_size = secp256k1_pippenger_scratch_size(i, bucket_window);
-            scratch = secp256k1_scratch_create(&ctx->error_callback, 0, scratch_size + PIPPENGER_SCRATCH_OBJECTS*ALIGNMENT);
+            scratch = secp256k1_scratch_create(&ctx->error_callback, scratch_size + PIPPENGER_SCRATCH_OBJECTS*ALIGNMENT);
         } else {
             size_t scratch_size = secp256k1_strauss_scratch_size(i);
-            scratch = secp256k1_scratch_create(&ctx->error_callback, 0, scratch_size + STRAUSS_SCRATCH_OBJECTS*ALIGNMENT);
+            scratch = secp256k1_scratch_create(&ctx->error_callback, scratch_size + STRAUSS_SCRATCH_OBJECTS*ALIGNMENT);
         }
         CHECK(secp256k1_ecmult_multi_var(&ctx->ecmult_ctx, scratch, &r, &scG, ecmult_multi_callback, &data, n_points));
         secp256k1_gej_add_var(&r, &r, &r2, NULL);
@@ -2900,14 +2903,14 @@
 
     test_secp256k1_pippenger_bucket_window_inv();
     test_ecmult_multi_pippenger_max_points();
-    scratch = secp256k1_scratch_create(&ctx->error_callback, 0, 819200);
+    scratch = secp256k1_scratch_create(&ctx->error_callback, 819200);
     test_ecmult_multi(scratch, secp256k1_ecmult_multi_var);
     test_ecmult_multi(scratch, secp256k1_ecmult_pippenger_batch_single);
     test_ecmult_multi(scratch, secp256k1_ecmult_strauss_batch_single);
     secp256k1_scratch_destroy(scratch);
 
     /* Run test_ecmult_multi with space for exactly one point */
-    scratch = secp256k1_scratch_create(&ctx->error_callback, 0, secp256k1_strauss_scratch_size(1) + STRAUSS_SCRATCH_OBJECTS*ALIGNMENT);
+    scratch = secp256k1_scratch_create(&ctx->error_callback, secp256k1_strauss_scratch_size(1) + STRAUSS_SCRATCH_OBJECTS*ALIGNMENT);
     test_ecmult_multi(scratch, secp256k1_ecmult_multi_var);
     secp256k1_scratch_destroy(scratch);
 
diff --git a/src/secp256k1/src/tests_exhaustive.c b/src/secp256k1/src/tests_exhaustive.c
--- a/src/secp256k1/src/tests_exhaustive.c
+++ b/src/secp256k1/src/tests_exhaustive.c
@@ -196,7 +196,7 @@
 
 void test_exhaustive_ecmult_multi(const secp256k1_context *ctx, const secp256k1_ge *group, int order) {
     int i, j, k, x, y;
-    secp256k1_scratch *scratch = secp256k1_scratch_create(&ctx->error_callback, 1024, 4096);
+    secp256k1_scratch *scratch = secp256k1_scratch_create(&ctx->error_callback, 4096);
     for (i = 0; i < order; i++) {
         for (j = 0; j < order; j++) {
             for (k = 0; k < order; k++) {