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
@@ -1152,16 +1152,18 @@
         return secp256k1_ecmult_multi_simple_var(ctx, r, inp_g_sc, cb, cbdata, n);
     }
 
-    /* Compute the batch sizes for pippenger given a scratch space. If it's greater than a threshold
-     * use pippenger. Otherwise use strauss */
+    /* Compute the batch sizes for Pippenger's algorithm given a scratch space. If it's greater than
+     * a threshold use Pippenger's algorithm. Otherwise use Strauss' algorithm.
+     * As a first step check if there's enough space for Pippenger's algo (which requires less space
+     * than Strauss' algo) and if not, use the simple algorithm. */
     if (!secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, secp256k1_pippenger_max_points(scratch), n)) {
-        return 0;
+        return secp256k1_ecmult_multi_simple_var(ctx, r, inp_g_sc, cb, cbdata, n);
     }
     if (n_batch_points >= ECMULT_PIPPENGER_THRESHOLD) {
         f = secp256k1_ecmult_pippenger_batch;
     } else {
         if (!secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, secp256k1_strauss_max_points(scratch), n)) {
-            return 0;
+            return secp256k1_ecmult_multi_simple_var(ctx, r, inp_g_sc, cb, cbdata, n);
         }
         f = secp256k1_ecmult_strauss_batch;
     }
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
@@ -2572,7 +2572,6 @@
     secp256k1_gej r;
     secp256k1_gej r2;
     ecmult_multi_data data;
-    secp256k1_scratch *scratch_empty;
 
     data.sc = sc;
     data.pt = pt;
@@ -2607,11 +2606,6 @@
         secp256k1_gej_add_var(&r, &r, &r2, NULL);
         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);
-        CHECK(!ecmult_multi(&ctx->ecmult_ctx, scratch_empty, &r, &szero, ecmult_multi_callback, &data, 1));
-        secp256k1_scratch_destroy(scratch_empty);
-
         /* Try to multiply 1 point, but callback returns false */
         CHECK(!ecmult_multi(&ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_false_callback, &data, 1));
 
@@ -2808,6 +2802,24 @@
     }
 }
 
+void test_ecmult_multi_batch_single(secp256k1_ecmult_multi_func ecmult_multi) {
+    secp256k1_scalar szero;
+    secp256k1_scalar sc[32];
+    secp256k1_ge pt[32];
+    secp256k1_gej r;
+    ecmult_multi_data data;
+    secp256k1_scratch *scratch_empty;
+
+    data.sc = sc;
+    data.pt = pt;
+    secp256k1_scalar_set_int(&szero, 0);
+
+    /* Try to multiply 1 point, but scratch space is empty.*/
+    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);
+}
+
 void test_secp256k1_pippenger_bucket_window_inv(void) {
     int i;
 
@@ -2931,19 +2943,25 @@
     }
     data.sc = sc;
     data.pt = pt;
+    secp256k1_gej_neg(&r2, &r2);
 
-    /* Test with empty scratch space */
+    /* Test with empty scratch space. It should compute the correct result using 
+     * ecmult_mult_simple algorithm which doesn't require a scratch space. */
     scratch = secp256k1_scratch_create(&ctx->error_callback, 0);
-    CHECK(!secp256k1_ecmult_multi_var(&ctx->ecmult_ctx, scratch, &r, &scG, ecmult_multi_callback, &data, 1));
+    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);
+    CHECK(secp256k1_gej_is_infinity(&r));
     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. */
+     * ecmult_multi selects strauss which requires more memory. It should
+     * therefore select the simple algorithm. */
     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));
+    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);
+    CHECK(secp256k1_gej_is_infinity(&r));
     secp256k1_scratch_destroy(scratch);
 
-    secp256k1_gej_neg(&r2, &r2);
     for(i = 1; i <= n_points; i++) {
         if (i > ECMULT_PIPPENGER_THRESHOLD) {
             int bucket_window = secp256k1_pippenger_bucket_window(i);
@@ -2971,7 +2989,9 @@
     test_ecmult_multi(scratch, secp256k1_ecmult_multi_var);
     test_ecmult_multi(NULL, secp256k1_ecmult_multi_var);
     test_ecmult_multi(scratch, secp256k1_ecmult_pippenger_batch_single);
+    test_ecmult_multi_batch_single(secp256k1_ecmult_pippenger_batch_single);
     test_ecmult_multi(scratch, secp256k1_ecmult_strauss_batch_single);
+    test_ecmult_multi_batch_single(secp256k1_ecmult_strauss_batch_single);
     secp256k1_scratch_destroy(scratch);
 
     /* Run test_ecmult_multi with space for exactly one point */