diff --git a/include/xsimd/arch/common/xsimd_common_details.hpp b/include/xsimd/arch/common/xsimd_common_details.hpp
index 0a8abc419..03088eec4 100644
--- a/include/xsimd/arch/common/xsimd_common_details.hpp
+++ b/include/xsimd/arch/common/xsimd_common_details.hpp
@@ -90,6 +90,9 @@ namespace xsimd
     XSIMD_INLINE std::pair<batch<T, A>, batch<T, A>> sincos(batch<T, A> const& self) noexcept;
     template <class T, class A>
     XSIMD_INLINE batch<T, A> sqrt(batch<T, A> const& self) noexcept;
+    template <class T, class A, class Vt, Vt... Values>
+    XSIMD_INLINE typename std::enable_if<std::is_arithmetic<T>::value, batch<T, A>>::type
+    swizzle(batch<T, A> const& x, batch_constant<Vt, A, Values...> mask) noexcept;
     template <class T, class A>
     XSIMD_INLINE batch<T, A> tan(batch<T, A> const& self) noexcept;
     template <class T, class A>
diff --git a/include/xsimd/arch/common/xsimd_common_memory.hpp b/include/xsimd/arch/common/xsimd_common_memory.hpp
index 812ad0bca..773177233 100644
--- a/include/xsimd/arch/common/xsimd_common_memory.hpp
+++ b/include/xsimd/arch/common/xsimd_common_memory.hpp
@@ -341,7 +341,7 @@ namespace xsimd
                 }
             };
 
-            return swizzle(self, make_batch_constant<as_unsigned_integer_t<T>, rotate_generator, A>(), A {});
+            return swizzle(self, make_batch_constant<as_unsigned_integer_t<T>, rotate_generator, A>());
         }
 
         template <size_t N, class A, class T>
@@ -362,7 +362,7 @@ namespace xsimd
                 }
             };
 
-            return swizzle(self, make_batch_constant<as_unsigned_integer_t<T>, rotate_generator, A>(), A {});
+            return swizzle(self, make_batch_constant<as_unsigned_integer_t<T>, rotate_generator, A>());
         }
 
         template <size_t N, class A, class T>
@@ -611,6 +611,15 @@ namespace xsimd
             return batch<T, A>::load_aligned(out_buffer);
         }
 
+        template <class A, class T, class ITy, ITy... Is>
+        XSIMD_INLINE batch<T, A> swizzle(batch<T, A> const& self, batch_constant<ITy, A, Is...>, requires_arch<common>) noexcept
+        {
+            constexpr size_t size = batch<T, A>::size;
+            alignas(A::alignment()) T self_buffer[size];
+            store_aligned(&self_buffer[0], self);
+            return { self_buffer[Is]... };
+        }
+
         template <class A, class T, class ITy>
         XSIMD_INLINE batch<std::complex<T>, A> swizzle(batch<std::complex<T>, A> const& self, batch<ITy, A> mask, requires_arch<common>) noexcept
         {
diff --git a/include/xsimd/arch/xsimd_avx2.hpp b/include/xsimd/arch/xsimd_avx2.hpp
index 3ab8517a9..0a17ce512 100644
--- a/include/xsimd/arch/xsimd_avx2.hpp
+++ b/include/xsimd/arch/xsimd_avx2.hpp
@@ -657,9 +657,35 @@ namespace xsimd
 
         // rotate_left
         template <size_t N, class A>
+        XSIMD_INLINE batch<uint8_t, A> rotate_left(batch<uint8_t, A> const& self, requires_arch<avx2>) noexcept
+        {
+            auto other = _mm256_permute2x128_si256(self, self, 0x1);
+            if (N < 16)
+            {
+                return _mm256_alignr_epi8(other, self, N);
+            }
+            else
+            {
+                return _mm256_alignr_epi8(self, other, N - 16);
+            }
+        }
+        template <size_t N, class A>
+        XSIMD_INLINE batch<int8_t, A> rotate_left(batch<int8_t, A> const& self, requires_arch<avx2>) noexcept
+        {
+            return bitwise_cast<int8_t>(rotate_left<N, A>(bitwise_cast<uint8_t>(self), avx2 {}));
+        }
+        template <size_t N, class A>
         XSIMD_INLINE batch<uint16_t, A> rotate_left(batch<uint16_t, A> const& self, requires_arch<avx2>) noexcept
         {
-            return _mm256_alignr_epi8(self, self, N);
+            auto other = _mm256_permute2x128_si256(self, self, 0x1);
+            if (N < 8)
+            {
+                return _mm256_alignr_epi8(other, self, 2 * N);
+            }
+            else
+            {
+                return _mm256_alignr_epi8(self, other, 2 * (N - 8));
+            }
         }
         template <size_t N, class A>
         XSIMD_INLINE batch<int16_t, A> rotate_left(batch<int16_t, A> const& self, requires_arch<avx2>) noexcept
@@ -876,6 +902,7 @@ namespace xsimd
         }
 
         // swizzle (dynamic mask)
+
         template <class A>
         XSIMD_INLINE batch<float, A> swizzle(batch<float, A> const& self, batch<uint32_t, A> mask, requires_arch<avx2>) noexcept
         {
diff --git a/include/xsimd/arch/xsimd_avx512bw.hpp b/include/xsimd/arch/xsimd_avx512bw.hpp
index 832cba6a1..0395853dc 100644
--- a/include/xsimd/arch/xsimd_avx512bw.hpp
+++ b/include/xsimd/arch/xsimd_avx512bw.hpp
@@ -429,18 +429,6 @@ namespace xsimd
             return detail::compare_int_avx512bw<A, T, _MM_CMPINT_NE>(self, other);
         }
 
-        // rotate_left
-        template <size_t N, class A>
-        XSIMD_INLINE batch<uint16_t, A> rotate_left(batch<uint16_t, A> const& self, requires_arch<avx512bw>) noexcept
-        {
-            return _mm512_alignr_epi8(self, self, N);
-        }
-        template <size_t N, class A>
-        XSIMD_INLINE batch<int16_t, A> rotate_left(batch<int16_t, A> const& self, requires_arch<avx512bw>) noexcept
-        {
-            return bitwise_cast<int16_t>(rotate_left<N, A>(bitwise_cast<uint16_t>(self), avx512bw {}));
-        }
-
         // sadd
         template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
         XSIMD_INLINE batch<T, A> sadd(batch<T, A> const& self, batch<T, A> const& other, requires_arch<avx512bw>) noexcept
diff --git a/include/xsimd/arch/xsimd_avx512f.hpp b/include/xsimd/arch/xsimd_avx512f.hpp
index dc46cd867..26947dffc 100644
--- a/include/xsimd/arch/xsimd_avx512f.hpp
+++ b/include/xsimd/arch/xsimd_avx512f.hpp
@@ -32,6 +32,8 @@ namespace xsimd
         XSIMD_INLINE batch<T, A> incr_if(batch<T, A> const& self, Mask const& mask, requires_arch<common>) noexcept;
         template <class A, class T, size_t I>
         XSIMD_INLINE batch<T, A> insert(batch<T, A> const& self, T val, index<I>, requires_arch<common>) noexcept;
+        template <class A, class T, class ITy, ITy... Is>
+        XSIMD_INLINE batch<T, A> swizzle(batch<T, A> const& self, batch_constant<ITy, A, Is...>, requires_arch<common>) noexcept;
         template <class A>
         XSIMD_INLINE void transpose(batch<uint16_t, A>* matrix_begin, batch<uint16_t, A>* matrix_end, requires_arch<common>) noexcept;
         template <class A>
diff --git a/include/xsimd/arch/xsimd_neon.hpp b/include/xsimd/arch/xsimd_neon.hpp
index ac3cdacd0..17642268d 100644
--- a/include/xsimd/arch/xsimd_neon.hpp
+++ b/include/xsimd/arch/xsimd_neon.hpp
@@ -2771,10 +2771,11 @@ namespace xsimd
         XSIMD_INLINE batch<T, A> rotate_left(batch<T, A> const& a, requires_arch<neon>) noexcept
         {
             using register_type = typename batch<T, A>::register_type;
+            // Adding modulo to avoid warning.
             const detail::neon_dispatcher::binary dispatcher = {
-                std::make_tuple(wrap::rotate_left_u8<N>, wrap::rotate_left_s8<N>, wrap::rotate_left_u16<N>, wrap::rotate_left_s16<N>,
-                                wrap::rotate_left_u32<N>, wrap::rotate_left_s32<N>, wrap::rotate_left_u64<N>, wrap::rotate_left_s64<N>,
-                                wrap::rotate_left_f32<N>)
+                std::make_tuple(wrap::rotate_left_u8<N>, wrap::rotate_left_s8<N>, wrap::rotate_left_u16<N % 8>, wrap::rotate_left_s16<N % 8>,
+                                wrap::rotate_left_u32<N % 4>, wrap::rotate_left_s32<N % 4>, wrap::rotate_left_u64<N % 2>, wrap::rotate_left_s64<N % 2>,
+                                wrap::rotate_left_f32<N % 4>)
             };
             return dispatcher.apply(register_type(a), register_type(a));
         }
diff --git a/include/xsimd/arch/xsimd_ssse3.hpp b/include/xsimd/arch/xsimd_ssse3.hpp
index b38e398b4..b612d438e 100644
--- a/include/xsimd/arch/xsimd_ssse3.hpp
+++ b/include/xsimd/arch/xsimd_ssse3.hpp
@@ -107,11 +107,22 @@ namespace xsimd
 
         // rotate_left
         template <size_t N, class A>
-        XSIMD_INLINE batch<uint16_t, A> rotate_left(batch<uint16_t, A> const& self, requires_arch<ssse3>) noexcept
+        XSIMD_INLINE batch<uint8_t, A> rotate_left(batch<uint8_t, A> const& self, requires_arch<ssse3>) noexcept
         {
             return _mm_alignr_epi8(self, self, N);
         }
         template <size_t N, class A>
+        XSIMD_INLINE batch<int8_t, A> rotate_left(batch<int8_t, A> const& self, requires_arch<ssse3>) noexcept
+        {
+            return bitwise_cast<int8_t>(rotate_left<N, A>(bitwise_cast<uint8_t>(self), ssse3 {}));
+        }
+
+        template <size_t N, class A>
+        XSIMD_INLINE batch<uint16_t, A> rotate_left(batch<uint16_t, A> const& self, requires_arch<ssse3>) noexcept
+        {
+            return _mm_alignr_epi8(self, self, 2 * N);
+        }
+        template <size_t N, class A>
         XSIMD_INLINE batch<int16_t, A> rotate_left(batch<int16_t, A> const& self, requires_arch<ssse3>) noexcept
         {
             return bitwise_cast<int16_t>(rotate_left<N, A>(bitwise_cast<uint16_t>(self), ssse3 {}));
diff --git a/test/test_batch_manip.cpp b/test/test_batch_manip.cpp
index 000491cd8..34c9c1032 100644
--- a/test/test_batch_manip.cpp
+++ b/test/test_batch_manip.cpp
@@ -20,7 +20,7 @@ namespace xsimd
     struct init_swizzle_base
     {
         using swizzle_vector_type = std::array<T, N>;
-        swizzle_vector_type lhs_in, exped_reverse, exped_fill, exped_dup, exped_ror, exped_rol;
+        swizzle_vector_type lhs_in, exped_reverse, exped_fill, exped_dup, exped_ror, exped_rol, exped_rol2;
 
         template <int... Indices>
         std::vector<swizzle_vector_type> create_swizzle_vectors()
@@ -42,12 +42,14 @@ namespace xsimd
                 exped_dup[i] = lhs_in[2 * (i / 2)];
                 exped_ror[i] = lhs_in[(i - 1) % N];
                 exped_rol[i] = lhs_in[(i + 1) % N];
+                exped_rol2[i] = lhs_in[(i + N - 1) % N];
             }
             vects.push_back(std::move(exped_reverse));
             vects.push_back(std::move(exped_fill));
             vects.push_back(std::move(exped_dup));
             vects.push_back(std::move(exped_ror));
             vects.push_back(std::move(exped_rol));
+            vects.push_back(std::move(exped_rol2));
 
             return vects;
         }
@@ -176,6 +178,20 @@ struct swizzle_test
         CHECK_BATCH_EQ(b_res, b_exped);
     }
 
+    void rotate_left_inv()
+    {
+        xsimd::init_swizzle_base<value_type, size> swizzle_base;
+        auto swizzle_vecs = swizzle_base.create_swizzle_vectors();
+        auto v_lhs = swizzle_vecs[0];
+        auto v_exped = swizzle_vecs[6];
+
+        B b_lhs = B::load_unaligned(v_lhs.data());
+        B b_exped = B::load_unaligned(v_exped.data());
+
+        B b_res = xsimd::rotate_left<size - 1>(b_lhs);
+        CHECK_BATCH_EQ(b_res, b_exped);
+    }
+
     void swizzle_reverse()
     {
         xsimd::init_swizzle_base<value_type, size> swizzle_base;
@@ -248,6 +264,7 @@ TEST_CASE_TEMPLATE("[swizzle]", B, BATCH_SWIZZLE_TYPES)
     SUBCASE("rotate")
     {
         Test.rotate_left();
+        Test.rotate_left_inv();
         Test.rotate_right();
     }
 
diff --git a/test/test_shuffle.cpp b/test/test_shuffle.cpp
index 1c7c9884b..bc89aafd5 100644
--- a/test/test_shuffle.cpp
+++ b/test/test_shuffle.cpp
@@ -561,13 +561,13 @@ struct shuffle_test
         CHECK_BATCH_EQ(b_res, b_ref);
     }
 
-    void swizzle()
+    void shuffle()
     {
         B b_lhs = B::load_unaligned(lhs.data());
         B b_rhs = B::load_unaligned(rhs.data());
 
         {
-            struct swizzle_lo_generator
+            struct shuffle_lo_generator
             {
                 static constexpr size_t get(size_t index, size_t size)
                 {
@@ -580,13 +580,13 @@ struct shuffle_test
                 ref[i] = lhs[size - i - 1];
             B b_ref = B::load_unaligned(ref.data());
 
-            INFO("swizzle first batch");
-            B b_res = xsimd::shuffle(b_lhs, b_rhs, xsimd::make_batch_constant<mask_type, swizzle_lo_generator, arch_type>());
+            INFO("shuffle first batch");
+            B b_res = xsimd::shuffle(b_lhs, b_rhs, xsimd::make_batch_constant<mask_type, shuffle_lo_generator, arch_type>());
             CHECK_BATCH_EQ(b_res, b_ref);
         }
 
         {
-            struct swizzle_hi_generator
+            struct shuffle_hi_generator
             {
                 static constexpr size_t get(size_t index, size_t size)
                 {
@@ -599,8 +599,8 @@ struct shuffle_test
                 ref[i] = rhs[size - i - 1];
             B b_ref = B::load_unaligned(ref.data());
 
-            INFO("swizzle second batch");
-            B b_res = xsimd::shuffle(b_lhs, b_rhs, xsimd::make_batch_constant<mask_type, swizzle_hi_generator, arch_type>());
+            INFO("shuffle second batch");
+            B b_res = xsimd::shuffle(b_lhs, b_rhs, xsimd::make_batch_constant<mask_type, shuffle_hi_generator, arch_type>());
             CHECK_BATCH_EQ(b_res, b_ref);
         }
     }
@@ -709,9 +709,9 @@ TEST_CASE_TEMPLATE("[shuffle]", B, BATCH_FLOAT_TYPES, xsimd::batch<uint32_t>, xs
     {
         Test.select();
     }
-    SUBCASE("swizzle")
+    SUBCASE("shuffle")
     {
-        Test.swizzle();
+        Test.shuffle();
     }
     SUBCASE("transpose")
     {
@@ -733,12 +733,12 @@ TEST_CASE_TEMPLATE("[small integer transpose]", B, xsimd::batch<uint16_t>, xsimd
 }
 
 #if (XSIMD_WITH_SSE2 && !XSIMD_WITH_AVX)
-TEST_CASE_TEMPLATE("[small integer swizzle]", B, xsimd::batch<uint16_t>, xsimd::batch<int16_t>)
+TEST_CASE_TEMPLATE("[small integer shuffle]", B, xsimd::batch<uint16_t>, xsimd::batch<int16_t>)
 {
     shuffle_test<B> Test;
-    SUBCASE("swizzle")
+    SUBCASE("shuffle")
     {
-        Test.swizzle();
+        Test.shuffle();
     }
 }
 #endif
diff --git a/test/test_utils.hpp b/test/test_utils.hpp
index 4b56dc01b..80914f331 100644
--- a/test/test_utils.hpp
+++ b/test/test_utils.hpp
@@ -591,13 +591,7 @@ namespace xsimd
 #define BATCH_TYPES BATCH_INT_TYPES, BATCH_FLOAT_TYPES
 #define BATCH_MATH_TYPES xsimd::batch<int32_t>, BATCH_FLOAT_TYPES
 
-#if !XSIMD_WITH_AVX || XSIMD_WITH_AVX2
-#define BATCH_SWIZZLE_TAIL , xsimd::batch<uint32_t>, xsimd::batch<int32_t>, xsimd::batch<uint64_t>, xsimd::batch<int64_t>
-#else
-#define BATCH_SWIZZLE_TAIL
-#endif
-
-#define BATCH_SWIZZLE_TYPES BATCH_FLOAT_TYPES, BATCH_COMPLEX_TYPES BATCH_SWIZZLE_TAIL
+#define BATCH_SWIZZLE_TYPES BATCH_FLOAT_TYPES, BATCH_COMPLEX_TYPES, BATCH_INT_TYPES
 
 /********************
  * conversion utils *