diff --git a/src/dft/backends/cufft/commit.cpp b/src/dft/backends/cufft/commit.cpp
index 91cd17971..923122f08 100644
--- a/src/dft/backends/cufft/commit.cpp
+++ b/src/dft/backends/cufft/commit.cpp
@@ -25,6 +25,7 @@
 
 #include <array>
 #include <algorithm>
+#include <iterator>
 #include <optional>
 
 #include "oneapi/math/exceptions.hpp"
@@ -160,9 +161,20 @@ class cufft_commit final : public dft::detail::commit_impl<prec, dom> {
         offset_bwd_in = stride_vecs.offset_bwd_in;
         offset_bwd_out = stride_vecs.offset_bwd_out;
 
-        // cufft ignores the first value in inembed and onembed, so there is no harm in putting offset there
-        auto a_min = std::min_element(stride_vecs.vec_a.begin() + 1, stride_vecs.vec_a.end());
-        auto b_min = std::min_element(stride_vecs.vec_b.begin() + 1, stride_vecs.vec_b.end());
+        // cufft ignores the first value in inembed and onembed, so there is no harm in putting offset there.
+        // Find the dimension with the smallest stride (used as the cuFFT istride/ostride). When several
+        // dimensions share the smallest stride - which happens when a dimension has extent 1 and hence the
+        // same stride as its neighbour - prefer the innermost (last) dimension. Searching in reverse makes
+        // std::min_element resolve such ties to the highest index, avoiding a spurious dimension swap below
+        // that would otherwise reject valid transforms (e.g. shapes like {3,1}). See issue #631.
+        auto a_min = std::min_element(std::make_reverse_iterator(stride_vecs.vec_a.end()),
+                                      std::make_reverse_iterator(stride_vecs.vec_a.begin() + 1))
+                         .base() -
+                     1;
+        auto b_min = std::min_element(std::make_reverse_iterator(stride_vecs.vec_b.end()),
+                                      std::make_reverse_iterator(stride_vecs.vec_b.begin() + 1))
+                         .base() -
+                     1;
         if constexpr (dom == dft::domain::REAL) {
             if ((a_min != stride_vecs.vec_a.begin() + rank) ||
                 (b_min != stride_vecs.vec_b.begin() + rank)) {
@@ -180,6 +192,8 @@ class cufft_commit final : public dft::detail::commit_impl<prec, dom> {
         }
         const int a_stride = static_cast<int>(*a_min);
         const int b_stride = static_cast<int>(*b_min);
+        // Capture the position before erasing, as the iterator is invalidated by erase.
+        const auto a_min_idx = a_min - stride_vecs.vec_a.begin();
         stride_vecs.vec_a.erase(a_min);
         stride_vecs.vec_b.erase(b_min);
         int fwd_istride = a_stride;
@@ -188,9 +202,9 @@ class cufft_commit final : public dft::detail::commit_impl<prec, dom> {
             stride_api_choice == dft::detail::stride_api::FB_STRIDES ? b_stride : a_stride;
         int bwd_ostride =
             stride_api_choice == dft::detail::stride_api::FB_STRIDES ? a_stride : b_stride;
-        if (a_min - stride_vecs.vec_a.begin() != rank) {
+        if (a_min_idx != rank) {
             // swap dimensions to have the last one have the smallest stride
-            std::swap(n_copy[a_min - stride_vecs.vec_a.begin() - 1], n_copy[rank - 1]);
+            std::swap(n_copy[a_min_idx - 1], n_copy[rank - 1]);
         }
         for (int i = 1; i < rank; i++) {
             if ((stride_vecs.vec_a[i] % a_stride != 0) || (stride_vecs.vec_b[i] % b_stride != 0)) {