diff --git a/src/AggregateFunctions/SingleValueData.cpp b/src/AggregateFunctions/SingleValueData.cpp
index 4c5ed86c206..dae5e80a38c 100644
--- a/src/AggregateFunctions/SingleValueData.cpp
+++ b/src/AggregateFunctions/SingleValueData.cpp
@@ -421,15 +421,7 @@ std::optional<size_t> SingleValueDataFixed<T>::getSmallestIndex(const IColumn &
     const auto & vec = assert_cast<const ColVecType &>(column);
     if constexpr (has_find_extreme_implementation<T>)
     {
-        std::optional<T> opt = findExtremeMin(vec.getData().data(), row_begin, row_end);
-        if (!opt || (has() && value <= opt))
-            return std::nullopt;
-
-        /// TODO: Implement findExtremeMinIndex to do the lookup properly (with SIMD and batching)
-        for (size_t i = row_begin; i < row_end; i++)
-            if (vec.getData()[i] == *opt)
-                return i;
-        return row_end;
+        return findExtremeMinIndex(vec.getData().data(), row_begin, row_end);
     }
     else
     {
@@ -450,15 +442,7 @@ std::optional<size_t> SingleValueDataFixed<T>::getGreatestIndex(const IColumn &
     const auto & vec = assert_cast<const ColVecType &>(column);
     if constexpr (has_find_extreme_implementation<T>)
     {
-        std::optional<T> opt = findExtremeMax(vec.getData().data(), row_begin, row_end);
-        if (!opt || (has() && value >= opt))
-            return std::nullopt;
-
-        /// TODO: Implement findExtremeMaxIndex to do the lookup properly (with SIMD and batching)
-        for (size_t i = row_begin; i < row_end; i++)
-            if (vec.getData()[i] == *opt)
-                return i;
-        return row_end;
+        return findExtremeMaxIndex(vec.getData().data(), row_begin, row_end);
     }
     else
     {
diff --git a/src/AggregateFunctions/SingleValueData.h b/src/AggregateFunctions/SingleValueData.h
index eb770595a1a..e216586bf09 100644
--- a/src/AggregateFunctions/SingleValueData.h
+++ b/src/AggregateFunctions/SingleValueData.h
@@ -57,8 +57,7 @@ struct SingleValueDataBase
     virtual void setGreatestNotNullIf(const IColumn &, const UInt8 * __restrict, const UInt8 * __restrict, size_t, size_t, Arena *);
 
     /// Given a column returns the index of the smallest or greatest value in it
-    /// Doesn't return anything if the column is empty. In some cases (SingleValueDataFixed<T>) it will also return
-    /// empty if the stored value is already the smallest/greatest
+    /// Doesn't return anything if the column is empty
     /// There are used to implement argMin / argMax
     virtual std::optional<size_t> getSmallestIndex(const IColumn & column, size_t row_begin, size_t row_end);
     virtual std::optional<size_t> getGreatestIndex(const IColumn & column, size_t row_begin, size_t row_end);
diff --git a/src/Columns/ColumnVector.cpp b/src/Columns/ColumnVector.cpp
index b1cf449dfde..b22d12b995f 100644
--- a/src/Columns/ColumnVector.cpp
+++ b/src/Columns/ColumnVector.cpp
@@ -19,6 +19,7 @@
 #include <Common/TargetSpecific.h>
 #include <Common/WeakHash.h>
 #include <Common/assert_cast.h>
+#include <Common/findExtreme.h>
 #include <Common/iota.h>
 
 #include <bit>
@@ -247,6 +248,26 @@ void ColumnVector<T>::getPermutation(IColumn::PermutationSortDirection direction
 
     iota(res.data(), data_size, IColumn::Permutation::value_type(0));
 
+    if constexpr (has_find_extreme_implementation<T> && !std::is_floating_point_v<T>)
+    {
+        /// Disabled for:floating point
+        /// * floating point: We don't deal with nan_direction_hint
+        /// * stability::Stable: We might return any value, not the first
+        if ((limit == 1) && (stability == IColumn::PermutationSortStability::Unstable))
+        {
+            std::optional<size_t> index;
+            if (direction == IColumn::PermutationSortDirection::Ascending)
+                index = findExtremeMinIndex(data.data(), 0, data.size());
+            else
+                index = findExtremeMaxIndex(data.data(), 0, data.size());
+            if (index)
+            {
+                res.data()[0] = *index;
+                return;
+            }
+        }
+    }
+
     if constexpr (is_arithmetic_v<T> && !is_big_int_v<T>)
     {
         if (!limit)
diff --git a/src/Common/findExtreme.cpp b/src/Common/findExtreme.cpp
index c02450e2adc..f7fc1c3cfea 100644
--- a/src/Common/findExtreme.cpp
+++ b/src/Common/findExtreme.cpp
@@ -133,14 +133,54 @@ std::optional<T> findExtremeMaxIf(const T * __restrict ptr, const UInt8 * __rest
     return findExtreme<T, MaxComparator<T>, false, false>(ptr, condition_map, start, end);
 }
 
+template <has_find_extreme_implementation T>
+std::optional<size_t> findExtremeMinIndex(const T * __restrict ptr, size_t start, size_t end)
+{
+    /// This is implemented based on findNumericExtreme and not the other way around (or independently) because getting
+    /// the MIN or MAX value of an array is possible with SIMD, but getting the index isn't.
+    /// So what we do is use SIMD to find the lowest value and then iterate again over the array to find its position
+    std::optional<T> opt = findExtremeMin(ptr, start, end);
+    if (!opt)
+        return std::nullopt;
+
+    /// Some minimal heuristics for the case the input is sorted
+    if (*opt == ptr[start])
+        return {start};
+    for (size_t i = end - 1; i != start + 1; i--)
+        if (ptr[i] == *opt)
+            return {i};
+    return std::nullopt;
+}
+
+template <has_find_extreme_implementation T>
+std::optional<size_t> findExtremeMaxIndex(const T * __restrict ptr, size_t start, size_t end)
+{
+    std::optional<T> opt = findExtremeMax(ptr, start, end);
+    if (!opt)
+        return std::nullopt;
+
+    /// Some minimal heuristics for the case the input is sorted
+    if (*opt == ptr[start])
+        return {start};
+    for (size_t i = end - 1; i != start + 1; i--)
+        if (ptr[i] == *opt)
+            return {i};
+    return std::nullopt;
+}
 
 #define INSTANTIATION(T) \
     template std::optional<T> findExtremeMin(const T * __restrict ptr, size_t start, size_t end); \
-    template std::optional<T> findExtremeMinNotNull(const T * __restrict ptr, const UInt8 * __restrict condition_map, size_t start, size_t end); \
-    template std::optional<T> findExtremeMinIf(const T * __restrict ptr, const UInt8 * __restrict condition_map, size_t start, size_t end); \
+    template std::optional<T> findExtremeMinNotNull( \
+        const T * __restrict ptr, const UInt8 * __restrict condition_map, size_t start, size_t end); \
+    template std::optional<T> findExtremeMinIf( \
+        const T * __restrict ptr, const UInt8 * __restrict condition_map, size_t start, size_t end); \
     template std::optional<T> findExtremeMax(const T * __restrict ptr, size_t start, size_t end); \
-    template std::optional<T> findExtremeMaxNotNull(const T * __restrict ptr, const UInt8 * __restrict condition_map, size_t start, size_t end); \
-    template std::optional<T> findExtremeMaxIf(const T * __restrict ptr, const UInt8 * __restrict condition_map, size_t start, size_t end);
+    template std::optional<T> findExtremeMaxNotNull( \
+        const T * __restrict ptr, const UInt8 * __restrict condition_map, size_t start, size_t end); \
+    template std::optional<T> findExtremeMaxIf( \
+        const T * __restrict ptr, const UInt8 * __restrict condition_map, size_t start, size_t end); \
+    template std::optional<size_t> findExtremeMinIndex(const T * __restrict ptr, size_t start, size_t end); \
+    template std::optional<size_t> findExtremeMaxIndex(const T * __restrict ptr, size_t start, size_t end);
 
 FOR_BASIC_NUMERIC_TYPES(INSTANTIATION)
 #undef INSTANTIATION
diff --git a/src/Common/findExtreme.h b/src/Common/findExtreme.h
index c43d2d43350..68e7360d6e2 100644
--- a/src/Common/findExtreme.h
+++ b/src/Common/findExtreme.h
@@ -31,15 +31,27 @@ std::optional<T> findExtremeMaxNotNull(const T * __restrict ptr, const UInt8 * _
 template <has_find_extreme_implementation T>
 std::optional<T> findExtremeMaxIf(const T * __restrict ptr, const UInt8 * __restrict condition_map, size_t start, size_t end);
 
+template <has_find_extreme_implementation T>
+std::optional<size_t> findExtremeMinIndex(const T * __restrict ptr, size_t start, size_t end);
+
+template <has_find_extreme_implementation T>
+std::optional<size_t> findExtremeMaxIndex(const T * __restrict ptr, size_t start, size_t end);
+
 #define EXTERN_INSTANTIATION(T) \
     extern template std::optional<T> findExtremeMin(const T * __restrict ptr, size_t start, size_t end); \
-    extern template std::optional<T> findExtremeMinNotNull(const T * __restrict ptr, const UInt8 * __restrict condition_map, size_t start, size_t end); \
-    extern template std::optional<T> findExtremeMinIf(const T * __restrict ptr, const UInt8 * __restrict condition_map, size_t start, size_t end); \
+    extern template std::optional<T> findExtremeMinNotNull( \
+        const T * __restrict ptr, const UInt8 * __restrict condition_map, size_t start, size_t end); \
+    extern template std::optional<T> findExtremeMinIf( \
+        const T * __restrict ptr, const UInt8 * __restrict condition_map, size_t start, size_t end); \
     extern template std::optional<T> findExtremeMax(const T * __restrict ptr, size_t start, size_t end); \
-    extern template std::optional<T> findExtremeMaxNotNull(const T * __restrict ptr, const UInt8 * __restrict condition_map, size_t start, size_t end); \
-    extern template std::optional<T> findExtremeMaxIf(const T * __restrict ptr, const UInt8 * __restrict condition_map, size_t start, size_t end);
+    extern template std::optional<T> findExtremeMaxNotNull( \
+        const T * __restrict ptr, const UInt8 * __restrict condition_map, size_t start, size_t end); \
+    extern template std::optional<T> findExtremeMaxIf( \
+        const T * __restrict ptr, const UInt8 * __restrict condition_map, size_t start, size_t end); \
+    extern template std::optional<size_t> findExtremeMinIndex(const T * __restrict ptr, size_t start, size_t end); \
+    extern template std::optional<size_t> findExtremeMaxIndex(const T * __restrict ptr, size_t start, size_t end);
 
-    FOR_BASIC_NUMERIC_TYPES(EXTERN_INSTANTIATION)
+FOR_BASIC_NUMERIC_TYPES(EXTERN_INSTANTIATION)
 #undef EXTERN_INSTANTIATION
 
 }
diff --git a/tests/performance/agg_functions_argmin_argmax.xml b/tests/performance/agg_functions_argmin_argmax.xml
new file mode 100644
index 00000000000..e8eed2a82de
--- /dev/null
+++ b/tests/performance/agg_functions_argmin_argmax.xml
@@ -0,0 +1,24 @@
+<test>
+    <substitutions>
+        <substitution>
+            <name>group_scale</name>
+            <values>
+                <value>1000000</value>
+            </values>
+        </substitution>
+    </substitutions>
+
+<query>select argMin(Title, EventTime) from hits_100m_single where Title != '' group by intHash32(UserID) % {group_scale} FORMAT Null</query>
+<query>select argMinIf(Title, EventTime, Title != '') from hits_100m_single group by intHash32(UserID) % {group_scale} FORMAT Null</query>
+<query>select argMinIf(Title::Nullable(String), EventTime::Nullable(DateTime), Title::Nullable(String) != '') from hits_100m_single group by intHash32(UserID) % {group_scale} FORMAT Null</query>
+
+<query>select argMin(RegionID, EventTime) from hits_100m_single where Title != '' group by intHash32(UserID) % {group_scale} FORMAT Null</query>
+<query>select argMin((Title, RegionID), EventTime) from hits_100m_single where Title != '' group by intHash32(UserID) % {group_scale} FORMAT Null</query>
+<query>select argMinIf(Title, EventTime, Title != '') from hits_100m_single group by intHash32(UserID) % {group_scale} FORMAT Null</query>
+
+<query>select argMax(WatchID, Age) from hits_100m_single FORMAT Null</query>
+<query>select argMax(WatchID, Age::Nullable(UInt8)) from hits_100m_single FORMAT Null</query>
+<query>select argMax(WatchID, (EventDate, EventTime)) from hits_100m_single where Title != '' group by intHash32(UserID) % {group_scale} FORMAT Null</query>
+<query>select argMax(MobilePhone, MobilePhoneModel) from hits_100m_single</query>
+
+</test>
diff --git a/tests/performance/order_with_limit.xml b/tests/performance/order_with_limit.xml
index 1e1cb52267c..d1ad2afade8 100644
--- a/tests/performance/order_with_limit.xml
+++ b/tests/performance/order_with_limit.xml
@@ -1,4 +1,5 @@
 <test>
+    <query>SELECT number AS n FROM numbers_mt(200000000) ORDER BY n DESC LIMIT 1 FORMAT Null</query>
     <query>SELECT number AS n FROM numbers_mt(200000000) ORDER BY n DESC LIMIT 10 FORMAT Null</query>
     <query>SELECT number AS n FROM numbers_mt(200000000) ORDER BY n DESC LIMIT 100 FORMAT Null</query>
     <query>SELECT number AS n FROM numbers_mt(200000000) ORDER BY n DESC LIMIT 1500 FORMAT Null</query>
@@ -7,6 +8,7 @@
     <query>SELECT number AS n FROM numbers_mt(200000000) ORDER BY n DESC LIMIT 10000 FORMAT Null</query>
     <query>SELECT number AS n FROM numbers_mt(200000000) ORDER BY n DESC LIMIT 65535 FORMAT Null</query>
 
+    <query>SELECT intHash64(number) AS n FROM numbers_mt(500000000) ORDER BY n LIMIT 1 FORMAT Null</query>
     <query>SELECT intHash64(number) AS n FROM numbers_mt(500000000) ORDER BY n LIMIT 10 FORMAT Null</query>
     <query>SELECT intHash64(number) AS n FROM numbers_mt(200000000) ORDER BY n LIMIT 100 FORMAT Null</query>
     <query>SELECT intHash64(number) AS n FROM numbers_mt(200000000) ORDER BY n LIMIT 1500 FORMAT Null</query>
@@ -15,6 +17,7 @@
     <query>SELECT intHash64(number) AS n FROM numbers_mt(200000000) ORDER BY n LIMIT 10000 FORMAT Null</query>
     <query>SELECT intHash64(number) AS n FROM numbers_mt(100000000) ORDER BY n LIMIT 65535 FORMAT Null</query>
 
+    <query>SELECT intHash64(number) AS n FROM numbers_mt(200000000) ORDER BY n, n + 1, n + 2 LIMIT 1 FORMAT Null</query>
     <query>SELECT intHash64(number) AS n FROM numbers_mt(200000000) ORDER BY n, n + 1, n + 2 LIMIT 10 FORMAT Null</query>
     <query>SELECT intHash64(number) AS n FROM numbers_mt(200000000) ORDER BY n, n + 1, n + 2 LIMIT 100 FORMAT Null</query>
     <query>SELECT intHash64(number) AS n FROM numbers_mt(200000000) ORDER BY n, n + 1, n + 2 LIMIT 1500 FORMAT Null</query>