diff --git a/include/xsimd/arch/xsimd_avx512f.hpp b/include/xsimd/arch/xsimd_avx512f.hpp
index 06da6218e..414a26f34 100644
--- a/include/xsimd/arch/xsimd_avx512f.hpp
+++ b/include/xsimd/arch/xsimd_avx512f.hpp
@@ -1962,25 +1962,19 @@ namespace xsimd
         }
 
         // reduce_max
-        template <class A, class T, class = std::enable_if_t<(sizeof(T) == 1)>>
+        template <class A, class T, class = std::enable_if_t<(sizeof(T) <= 2)>>
         XSIMD_INLINE T reduce_max(batch<T, A> const& self, requires_arch<avx512f>) noexcept
         {
-            constexpr batch_constant<uint64_t, A, 5, 6, 7, 8, 0, 0, 0, 0> mask;
-            batch<T, A> step = _mm512_permutexvar_epi64(mask.as_batch(), self);
-            batch<T, A> acc = max(self, step);
-            __m256i low = _mm512_castsi512_si256(acc);
-            return reduce_max(batch<T, avx2>(low));
+            batch<T, avx2> low(detail::lower_half(self)), high(detail::upper_half(self));
+            return reduce_max(max(low, high));
         }
 
         // reduce_min
-        template <class A, class T, class = std::enable_if_t<(sizeof(T) == 1)>>
+        template <class A, class T, class = std::enable_if_t<(sizeof(T) <= 2)>>
         XSIMD_INLINE T reduce_min(batch<T, A> const& self, requires_arch<avx512f>) noexcept
         {
-            constexpr batch_constant<uint64_t, A, 5, 6, 7, 8, 0, 0, 0, 0> mask;
-            batch<T, A> step = _mm512_permutexvar_epi64(mask.as_batch(), self);
-            batch<T, A> acc = min(self, step);
-            __m256i low = _mm512_castsi512_si256(acc);
-            return reduce_min(batch<T, avx2>(low));
+            batch<T, avx2> low(detail::lower_half(self)), high(detail::upper_half(self));
+            return reduce_min(min(low, high));
         }
 
         // reduce_mul
diff --git a/test/test_batch.cpp b/test/test_batch.cpp
index 0bee8b1fc..3ee94ee4f 100644
--- a/test/test_batch.cpp
+++ b/test/test_batch.cpp
@@ -1070,6 +1070,22 @@ struct batch_test
             INFO("reduce_min");
             CHECK_SCALAR_EQ(res, expected);
         }
+        // reduce_max / reduce_min with the extremum at each position
+        for (std::size_t i = 0; i < size; ++i)
+        {
+            array_type data;
+            data.fill(value_type(1));
+            {
+                data[i] = std::numeric_limits<value_type>::max();
+                INFO("reduce_max, extremum at index ", i);
+                CHECK_SCALAR_EQ(reduce_max(batch_type::load_unaligned(data.data())), data[i]);
+            }
+            {
+                data[i] = std::numeric_limits<value_type>::lowest();
+                INFO("reduce_min, extremum at index ", i);
+                CHECK_SCALAR_EQ(reduce_min(batch_type::load_unaligned(data.data())), data[i]);
+            }
+        }
         // reduce_mul
         {
             value_type expected = std::accumulate(lhs.cbegin(), lhs.cend(), value_type(1), std::multiplies<value_type>());