diff --git a/include/xsimd/arch/utils/shifts.hpp b/include/xsimd/arch/utils/shifts.hpp
new file mode 100644
index 000000000..ac93ed336
--- /dev/null
+++ b/include/xsimd/arch/utils/shifts.hpp
@@ -0,0 +1,89 @@
+/***************************************************************************
+ * Copyright (c) Johan Mabille, Sylvain Corlay, Wolf Vollprecht and         *
+ * Martin Renou                                                             *
+ * Copyright (c) QuantStack                                                 *
+ * Copyright (c) Serge Guelton                                              *
+ * Copyright (c) Marco Barbone                                              *
+ *                                                                          *
+ * Distributed under the terms of the BSD 3-Clause License.                 *
+ *                                                                          *
+ * The full license is in the file LICENSE, distributed with this software. *
+ ****************************************************************************/
+
+#ifndef XSIMD_UTILS_SHIFTS_HPP
+#define XSIMD_UTILS_SHIFTS_HPP
+
+#include "../../config/xsimd_inline.hpp"
+#include "../../types/xsimd_batch.hpp"
+#include "../../types/xsimd_batch_constant.hpp"
+
+namespace xsimd
+{
+    namespace kernel
+    {
+        namespace utils
+        {
+            template <typename I, I offset, I length, I... Vs>
+            struct select_stride
+            {
+                static constexpr I values_array[] = { Vs... };
+
+                template <typename K>
+                static constexpr K get(K i, K)
+                {
+                    return static_cast<K>(values_array[length * i + offset]);
+                }
+            };
+
+            template <typename I>
+            constexpr I lsb_mask(I bit_index)
+            {
+                if (bit_index == 8 * sizeof(I))
+                {
+                    return ~I { 0 };
+                }
+                return static_cast<I>((I { 1 } << bit_index) - I { 1 });
+            }
+
+            template <class T, class A, T... Vs>
+            constexpr bool all_equals(batch_constant<T, A, Vs...> c)
+            {
+                static_assert(sizeof...(Vs) > 0, "There must be at least one value");
+
+                bool out = true;
+                for (std::size_t k = 0; k < sizeof...(Vs); ++k)
+                {
+                    out &= c.get(k) == c.get(0);
+                }
+                return out;
+            }
+
+            template <class T, class T2, class A, T... Vs>
+            XSIMD_INLINE batch<T, A> bitwise_lshift_as_twice_larger(
+                batch<T, A> const& self, batch_constant<T, A, Vs...>) noexcept
+            {
+                static_assert(sizeof(T2) == 2 * sizeof(T), "One size must be twice the other");
+
+                const auto self2 = bitwise_cast<T2>(self);
+
+                // Lower byte: shift as twice the size and mask bits flowing to higher byte.
+                constexpr auto shifts_lo = make_batch_constant<T2, select_stride<T, 0, 2, Vs...>, A>();
+                constexpr auto mask_lo = lsb_mask<T2>(8 * sizeof(T));
+                const auto shifted_lo = bitwise_lshift(self2, shifts_lo);
+                constexpr auto batch_mask_lo = make_batch_constant<T2, mask_lo, A>();
+                const auto masked_lo = bitwise_and(shifted_lo, batch_mask_lo.as_batch());
+
+                // Higher byte: mask bits that would flow from lower byte and shift as twice the size.
+                constexpr auto shifts_hi = make_batch_constant<T2, select_stride<T, 1, 2, Vs...>, A>();
+                constexpr auto mask_hi = mask_lo << (8 * sizeof(T));
+                constexpr auto batch_mask_hi = make_batch_constant<T2, mask_hi, A>();
+                const auto masked_hi = bitwise_and(self2, batch_mask_hi.as_batch());
+                const auto shifted_hi = bitwise_lshift(masked_hi, shifts_hi);
+
+                return bitwise_cast<T>(bitwise_or(masked_lo, shifted_hi));
+            }
+        }
+    }
+}
+
+#endif
diff --git a/include/xsimd/arch/xsimd_avx2.hpp b/include/xsimd/arch/xsimd_avx2.hpp
index bf6d9e7de..54485b5ef 100644
--- a/include/xsimd/arch/xsimd_avx2.hpp
+++ b/include/xsimd/arch/xsimd_avx2.hpp
@@ -17,6 +17,7 @@
 
 #include "../types/xsimd_avx2_register.hpp"
 #include "../types/xsimd_batch_constant.hpp"
+#include "./utils/shifts.hpp"
 
 #include <limits>
 
@@ -332,6 +333,40 @@ namespace xsimd
             }
         }
 
+        // bitwise_lshift multiple (constant) specific implementations.
+        // Missing implementations are dispacthed to the `batch` overload in xsimd_api.
+        template <class T, class A, T... Vs, detail::enable_sized_integral_t<T, 2> = 0>
+        XSIMD_INLINE batch<T, A> bitwise_lshift(
+            batch<T, A> const& self, batch_constant<T, A, Vs...> shifts, requires_arch<avx2> req) noexcept
+        {
+            using uint_t = typename std::make_unsigned<T>::type;
+
+            XSIMD_IF_CONSTEXPR(utils::all_equals(shifts))
+            {
+                return bitwise_lshift<shifts.get(0), A>(self, req);
+            }
+            return bitwise_cast<T>(
+                utils::bitwise_lshift_as_twice_larger<uint_t, uint32_t>(
+                    bitwise_cast<uint_t>(self),
+                    batch_constant<uint_t, A, static_cast<uint_t>(Vs)...> {}));
+        }
+
+        template <class T, class A, T... Vs, detail::enable_sized_integral_t<T, 1> = 0>
+        XSIMD_INLINE batch<T, A> bitwise_lshift(
+            batch<T, A> const& self, batch_constant<T, A, Vs...> shifts, requires_arch<avx2> req) noexcept
+        {
+            using uint_t = typename std::make_unsigned<T>::type;
+
+            XSIMD_IF_CONSTEXPR(utils::all_equals(shifts))
+            {
+                return bitwise_lshift<shifts.get(0), A>(self, req);
+            }
+            return bitwise_cast<T>(
+                utils::bitwise_lshift_as_twice_larger<uint_t, uint16_t>(
+                    bitwise_cast<uint_t>(self),
+                    batch_constant<uint_t, A, static_cast<uint_t>(Vs)...> {}));
+        }
+
         // bitwise_or
         template <class A, class T, class = std::enable_if_t<std::is_integral<T>::value>>
         XSIMD_INLINE batch<T, A> bitwise_or(batch<T, A> const& self, batch<T, A> const& other, requires_arch<avx2>) noexcept
diff --git a/include/xsimd/arch/xsimd_sse2.hpp b/include/xsimd/arch/xsimd_sse2.hpp
index cccba8144..fdd6611e1 100644
--- a/include/xsimd/arch/xsimd_sse2.hpp
+++ b/include/xsimd/arch/xsimd_sse2.hpp
@@ -18,6 +18,7 @@
 
 #include "../types/xsimd_batch_constant.hpp"
 #include "../types/xsimd_sse2_register.hpp"
+#include "./utils/shifts.hpp"
 
 namespace xsimd
 {
@@ -326,6 +327,36 @@ namespace xsimd
             return bitwise_lshift<shift>(self, common {});
         }
 
+        // bitwise_lshift multiple (constant)
+        // Missing implementations are dispacthed to the `batch` overload in xsimd_api.
+        template <class T, class A, T... Vs, detail::enable_sized_integral_t<T, 2> = 0>
+        XSIMD_INLINE batch<T, A> bitwise_lshift(
+            batch<T, A> const& self, batch_constant<T, A, Vs...> shifts, requires_arch<sse2> req) noexcept
+        {
+            XSIMD_IF_CONSTEXPR(utils::all_equals(shifts))
+            {
+                return bitwise_lshift<shifts.get(0), A>(self, req);
+            }
+            constexpr auto mults = batch_constant<T, A, static_cast<T>(1u << Vs)...>();
+            return _mm_mullo_epi16(self, mults.as_batch());
+        }
+
+        template <class T, class A, T... Vs, detail::enable_sized_integral_t<T, 1> = 0>
+        XSIMD_INLINE batch<T, A> bitwise_lshift(
+            batch<T, A> const& self, batch_constant<T, A, Vs...> shifts, requires_arch<sse2> req) noexcept
+        {
+            using uint_t = typename std::make_unsigned<T>::type;
+
+            XSIMD_IF_CONSTEXPR(utils::all_equals(shifts))
+            {
+                return bitwise_lshift<shifts.get(0), A>(self, req);
+            }
+            return bitwise_cast<T>(
+                utils::bitwise_lshift_as_twice_larger<uint_t, uint16_t>(
+                    bitwise_cast<uint_t>(self),
+                    batch_constant<uint_t, A, static_cast<uint_t>(Vs)...> {}));
+        }
+
         // bitwise_not
         template <class A>
         XSIMD_INLINE batch<float, A> bitwise_not(batch<float, A> const& self, requires_arch<sse2>) noexcept
diff --git a/include/xsimd/arch/xsimd_sse4_1.hpp b/include/xsimd/arch/xsimd_sse4_1.hpp
index 030fb29db..e6102bb6f 100644
--- a/include/xsimd/arch/xsimd_sse4_1.hpp
+++ b/include/xsimd/arch/xsimd_sse4_1.hpp
@@ -41,6 +41,15 @@ namespace xsimd
             return _mm_ceil_pd(self);
         }
 
+        // bitwise_lshift multiple (constant)
+        template <class A, uint32_t... Vs>
+        XSIMD_INLINE batch<uint32_t, A> bitwise_lshift(
+            batch<uint32_t, A> const& self, batch_constant<uint32_t, A, Vs...>, requires_arch<sse4_1>) noexcept
+        {
+            constexpr auto mults = batch_constant<uint32_t, A, static_cast<uint32_t>(1u << Vs)...>();
+            return _mm_mullo_epi32(self, mults.as_batch());
+        }
+
         // fast_cast
         namespace detail
         {
diff --git a/include/xsimd/types/xsimd_api.hpp b/include/xsimd/types/xsimd_api.hpp
index aa64df4da..abdb385ae 100644
--- a/include/xsimd/types/xsimd_api.hpp
+++ b/include/xsimd/types/xsimd_api.hpp
@@ -353,6 +353,41 @@ namespace xsimd
         return kernel::bitwise_cast<A>(x, batch<T_out, A> {}, A {});
     }
 
+    namespace detail
+    {
+        // Detection for kernel overloads accepting ``batch_constant`` in ``bitwise_lshift``
+        // directly (or in a parent register function).
+        // The ``batch_constant`` overload is a rare but useful optimization.
+        // Running the detection here is less error prone than to add a fallback to all
+        // architectures.
+
+        template <class A, class B, class C, class = void>
+        struct has_bitwise_lshift_batch_const : std::false_type
+        {
+        };
+
+        template <class A, class B, class C>
+        struct has_bitwise_lshift_batch_const<A, B, C,
+                                              void_t<decltype(kernel::bitwise_lshift<A>(std::declval<B>(), std::declval<C>(), A {}))>>
+            : std::true_type
+        {
+        };
+
+        template <class A, class T, T... Values>
+        XSIMD_INLINE batch<T, A> bitwise_lshift_batch_const(batch<T, A> const& x, batch_constant<T, A, Values...> shift, std::true_type) noexcept
+        {
+            // Optimized ``batch_constant`` implementation
+            return kernel::bitwise_lshift<A>(x, shift, A {});
+        }
+
+        template <class A, class T, T... Values>
+        XSIMD_INLINE batch<T, A> bitwise_lshift_batch_const(batch<T, A> const& x, batch_constant<T, A, Values...> shift, std::false_type) noexcept
+        {
+            // Fallback to regular run-time implementation
+            return kernel::bitwise_lshift<A>(x, shift.as_batch(), A {});
+        }
+    }
+
     /**
      * @ingroup batch_bitwise
      *
@@ -367,17 +402,24 @@ namespace xsimd
         detail::static_check_supported_config<T, A>();
         return kernel::bitwise_lshift<A>(x, shift, A {});
     }
+    template <size_t shift, class T, class A>
+    XSIMD_INLINE batch<T, A> bitwise_lshift(batch<T, A> const& x) noexcept
+    {
+        detail::static_check_supported_config<T, A>();
+        return kernel::bitwise_lshift<shift, A>(x, A {});
+    }
     template <class T, class A>
     XSIMD_INLINE batch<T, A> bitwise_lshift(batch<T, A> const& x, batch<T, A> const& shift) noexcept
     {
         detail::static_check_supported_config<T, A>();
         return kernel::bitwise_lshift<A>(x, shift, A {});
     }
-    template <size_t shift, class T, class A>
-    XSIMD_INLINE batch<T, A> bitwise_lshift(batch<T, A> const& x) noexcept
+    template <class T, class A, T... Values>
+    XSIMD_INLINE batch<T, A> bitwise_lshift(batch<T, A> const& x, batch_constant<T, A, Values...> shift) noexcept
     {
         detail::static_check_supported_config<T, A>();
-        return kernel::bitwise_lshift<shift, A>(x, A {});
+        using has_batch_const_impl = detail::has_bitwise_lshift_batch_const<A, decltype(x), decltype(shift)>;
+        return detail::bitwise_lshift_batch_const<A>(x, shift, has_batch_const_impl {});
     }
 
     /**
diff --git a/test/test_xsimd_api.cpp b/test/test_xsimd_api.cpp
index 8c58543ad..87386eb5e 100644
--- a/test/test_xsimd_api.cpp
+++ b/test/test_xsimd_api.cpp
@@ -351,7 +351,7 @@ struct xsimd_api_integral_types_functions
 {
     using value_type = typename scalar_type<T>::type;
 
-    void test_bitwise_lshift()
+    void test_bitwise_lshift_single()
     {
         constexpr int shift = 3;
         value_type val0(12);
@@ -364,6 +364,35 @@ struct xsimd_api_integral_types_functions
         CHECK_EQ(extract(cr), r);
     }
 
+    /* Test when T is a batch_constant only, not a scalar. */
+    template <typename U = T>
+    void test_bitwise_lshift_multiple(T const& vals, typename std::enable_if<!std::is_integral<U>::value, int>::type = 0)
+    {
+#ifndef XSIMD_NO_SUPPORTED_ARCHITECTURE
+        constexpr auto Max = static_cast<value_type>(std::numeric_limits<value_type>::digits);
+        constexpr auto max_batch = xsimd::make_batch_constant<value_type, Max>();
+        constexpr auto shifts = xsimd::make_iota_batch_constant<value_type>() % max_batch;
+
+        {
+            auto shifted = xsimd::bitwise_lshift(vals, shifts.as_batch());
+            auto shifted_cst = xsimd::bitwise_lshift(vals, shifts);
+
+            for (std::size_t i = 0; i < shifts.size; ++i)
+            {
+                const auto expected = static_cast<value_type>(vals.get(i) << shifts.get(i));
+                CHECK_EQ(shifted.get(i), expected);
+                CHECK_EQ(shifted_cst.get(i), expected);
+            }
+        }
+#endif
+    }
+
+    /* Test multiple does not make sense when T is scalar. */
+    template <typename U = T>
+    void test_bitwise_lshift_multiple(T const&, typename std::enable_if<std::is_integral<U>::value, int>::type = 0)
+    {
+    }
+
     void test_bitwise_rshift()
     {
         constexpr int shift = 3;
@@ -424,11 +453,20 @@ struct xsimd_api_integral_types_functions
 
 TEST_CASE_TEMPLATE("[xsimd api | integral types functions]", B, INTEGRAL_TYPES)
 {
-    xsimd_api_integral_types_functions<B> Test;
+    using test_type = xsimd_api_integral_types_functions<B>;
+
+    test_type Test;
+
+    SUBCASE("test_bitwise_lshift_single")
+    {
+        Test.test_bitwise_lshift_single();
+    }
 
-    SUBCASE("bitwise_lshift")
+    SUBCASE("bitwise_lshift_multiple")
     {
-        Test.test_bitwise_lshift();
+        Test.test_bitwise_lshift_multiple({ 1 });
+        Test.test_bitwise_lshift_multiple({ 3 });
+        Test.test_bitwise_lshift_multiple({ 127 });
     }
 
     SUBCASE("bitwise_rshift")