diff --git a/src/Core/MergeSelectorAlgorithm.h b/src/Core/MergeSelectorAlgorithm.h
index 0f6831c1f9e..8af23d0f885 100644
--- a/src/Core/MergeSelectorAlgorithm.h
+++ b/src/Core/MergeSelectorAlgorithm.h
@@ -8,6 +8,7 @@ enum class MergeSelectorAlgorithm : uint8_t
 {
     SIMPLE,
     STOCHASTIC_SIMPLE,
+    COMPLEX,
 };
 
 }
diff --git a/src/Storages/MergeTree/MergeSelectors/ComplexMergeSelector.cpp b/src/Storages/MergeTree/MergeSelectors/ComplexMergeSelector.cpp
new file mode 100644
index 00000000000..e988835116f
--- /dev/null
+++ b/src/Storages/MergeTree/MergeSelectors/ComplexMergeSelector.cpp
@@ -0,0 +1,127 @@
+#include <Storages/MergeTree/MergeSelectors/ComplexMergeSelector.h>
+#include <Storages/MergeTree/MergeSelectors/MergeSelectorFactory.h>
+#include <Core/MergeSelectorAlgorithm.h>
+
+#include <base/interpolate.h>
+#include <Common/thread_local_rng.h>
+
+#include <cmath>
+#include <cassert>
+
+
+namespace DB
+{
+
+void registerComplexMergeSelector(MergeSelectorFactory & factory)
+{
+    factory.registerPublicSelector("Complex", MergeSelectorAlgorithm::COMPLEX, [](const std::any & settings)
+    {
+        return std::make_shared<ComplexMergeSelector>(std::any_cast<ComplexMergeSelector::Settings>(settings));
+    });
+}
+
+namespace
+{
+
+/** Estimates best set of parts to merge within passed alternatives.
+  */
+struct Estimator
+{
+    using Iterator = ComplexMergeSelector::PartsRange::const_iterator;
+
+    void consider(Iterator begin, Iterator end, size_t sum_size, double sum_size_log_size, const ComplexMergeSelector::Settings &)
+    {
+        double current_score = score(sum_size, sum_size_log_size);
+
+        if (max_score == 0.0 || current_score > max_score)
+        {
+            max_score = current_score;
+            best_begin = begin;
+            best_end = end;
+        }
+    }
+
+    ComplexMergeSelector::PartsRange getBest() const
+    {
+        return ComplexMergeSelector::PartsRange(best_begin, best_end);
+    }
+
+    static double score(double sum_size, double sum_size_log_size)
+    {
+        // TODO(serxa): check what is faster log or log2
+        // TODO(serxa): add comment explaining why entropy maximization is the goal
+        return log2(sum_size) - sum_size_log_size / sum_size;
+    }
+
+    double max_score = 0.0;
+    Iterator best_begin {};
+    Iterator best_end {};
+};
+
+void selectWithinPartition(
+    const ComplexMergeSelector::PartsRange & parts,
+    const size_t max_total_size_to_merge,
+    Estimator & estimator,
+    const ComplexMergeSelector::Settings & settings)
+{
+    size_t parts_count = parts.size();
+    if (parts_count <= 1)
+        return;
+
+    for (size_t begin = 0; begin < parts_count; ++begin)
+    {
+        if (!parts[begin].shall_participate_in_merges)
+            continue;
+
+        // TODO(serxa): optimize out unnecessary log2() calls
+        size_t sum_size = parts[begin].size;
+        double sum_size_log_size = parts[begin].size * log2(parts[begin].size);
+        size_t max_size = parts[begin].size;
+        size_t min_age = parts[begin].age;
+
+        for (size_t end = begin + 2; end <= parts_count; ++end)
+        {
+            assert(end > begin);
+            if (settings.max_parts_to_merge_at_once && end - begin > settings.max_parts_to_merge_at_once)
+                break;
+
+            if (!parts[end - 1].shall_participate_in_merges)
+                break;
+
+            size_t cur_size = parts[end - 1].size;
+            size_t cur_age = parts[end - 1].age;
+
+            sum_size += cur_size;
+            sum_size_log_size += cur_size * log2(cur_size);
+            max_size = std::max(max_size, cur_size);
+            min_age = std::min(min_age, cur_age);
+
+            if (max_total_size_to_merge && sum_size > max_total_size_to_merge)
+                break;
+
+            // TODO(serxa): add constraint to control write amplification
+            estimator.consider(
+                parts.begin() + begin,
+                parts.begin() + end,
+                sum_size,
+                sum_size_log_size,
+                settings);
+        }
+    }
+}
+
+}
+
+ComplexMergeSelector::PartsRange ComplexMergeSelector::select(
+    const PartsRanges & parts_ranges,
+    size_t max_total_size_to_merge)
+{
+    Estimator estimator;
+
+    for (const auto & part_range : parts_ranges)
+        selectWithinPartition(part_range, max_total_size_to_merge, estimator, settings);
+
+    return estimator.getBest();
+}
+
+}
diff --git a/src/Storages/MergeTree/MergeSelectors/ComplexMergeSelector.h b/src/Storages/MergeTree/MergeSelectors/ComplexMergeSelector.h
new file mode 100644
index 00000000000..8ec45a754f6
--- /dev/null
+++ b/src/Storages/MergeTree/MergeSelectors/ComplexMergeSelector.h
@@ -0,0 +1,28 @@
+#pragma once
+
+#include <Storages/MergeTree/MergeSelectors/MergeSelector.h>
+
+
+namespace DB
+{
+
+class ComplexMergeSelector final : public IMergeSelector
+{
+public:
+    struct Settings
+    {
+        /// Zero means unlimited. Can be overridden by the same merge tree setting.
+        size_t max_parts_to_merge_at_once = 100;
+    };
+
+    explicit ComplexMergeSelector(const Settings & settings_) : settings(settings_) {}
+
+    PartsRange select(
+        const PartsRanges & parts_ranges,
+        size_t max_total_size_to_merge) override;
+
+private:
+    const Settings settings;
+};
+
+}