diff --git a/CMakeLists.txt b/CMakeLists.txt
index f95d5ff7..ea4217e6 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -317,6 +317,7 @@ set(DREAVM_TEST_SOURCES
   ${DREAVM_SOURCES}
   test/test_interval_tree.cc
   test/test_intrusive_list.cc
+  test/test_minmax_heap.cc
   test/test_ring_buffer.cc
   test/test_sh4.cc
   ${asm_inc})
diff --git a/src/core/minmax_heap.h b/src/core/minmax_heap.h
new file mode 100644
index 00000000..3f0424d4
--- /dev/null
+++ b/src/core/minmax_heap.h
@@ -0,0 +1,288 @@
+#ifndef MINMAX_HEAP_H
+#define MINMAX_HEAP_H
+
+#include <algorithm>
+#include <type_traits>
+#include "core/assert.h"
+
+// Min-max heap implementation, based on
+// http://www.akira.ruc.dk/~keld/teaching/algoritmedesign_f03/Artikler/02../Atkinson86.pdf
+
+namespace dvm {
+
+template <typename T>
+static inline bool mmheap_is_max_level(T index) {
+  T n = index + 1;
+  T log2 = 0;
+  while (n >>= 1) log2++;
+  return log2 % 2 == 1;
+}
+
+template <typename T>
+static inline T mmheap_parent(T index) {
+  return (index - 1) / 2;
+}
+
+template <typename T>
+static inline T mmheap_grandparent(T index) {
+  return mmheap_parent(mmheap_parent(index));
+}
+
+template <typename T>
+static inline bool mmheap_has_grandparent(T index) {
+  return mmheap_parent(index) != 0;
+}
+
+template <typename T>
+static inline T mmheap_left_child(T index) {
+  return 2 * index + 1;
+}
+
+template <typename T>
+static inline T mmheap_left_grandchild(T index) {
+  return mmheap_left_child(mmheap_left_child(index));
+}
+
+template <typename T>
+static inline T mmheap_is_child(T parent, T child) {
+  return parent == ((child - 1) / 2);
+}
+
+template <typename RandomIt, typename Compare>
+void mmheap_sift_up(
+    RandomIt first, RandomIt last, Compare comp,
+    typename std::iterator_traits<RandomIt>::difference_type index) {
+  using difference_type =
+      typename std::iterator_traits<RandomIt>::difference_type;
+
+  // can't sift up past the root
+  if (!index) {
+    return;
+  }
+
+  difference_type ancestor_index = mmheap_parent(index);
+  bool max_level = mmheap_is_max_level(ancestor_index);
+
+  // if the node is smaller (greater) than its parent, then it is smaller
+  // (greater) than all other nodes at max (min) levels up to the root. swap
+  // the node with its parent and check min (max) levels up to the root until
+  // the min-max order property is satisfied
+  if (comp(*(first + index), *(first + ancestor_index)) ^ max_level) {
+    std::swap(*(first + ancestor_index), *(first + index));
+    index = ancestor_index;
+  }
+  // if the node is greater (smaller) than its parent, then it is greater
+  // (smaller) than all other nodes at min (max) levels up to the root. the
+  // node is in the correct order with regards to its parent, but check max
+  // (min) levels up to the root until the min-max order property is satisfied
+  else {
+    max_level = !max_level;
+  }
+
+  while (mmheap_has_grandparent(index)) {
+    ancestor_index = mmheap_grandparent(index);
+
+    // once node is greater (smaller) than parent, the min-max order property
+    // is satisfied
+    if (!(comp(*(first + index), *(first + ancestor_index)) ^ max_level)) {
+      break;
+    }
+
+    // swap node with parent
+    std::swap(*(first + ancestor_index), *(first + index));
+    index = ancestor_index;
+  }
+}
+
+template <typename RandomIt, typename Compare>
+void mmheap_sift_down(
+    RandomIt first, RandomIt last, Compare comp,
+    typename std::iterator_traits<RandomIt>::difference_type index) {
+  using difference_type =
+      typename std::iterator_traits<RandomIt>::difference_type;
+
+  bool max_level = mmheap_is_max_level(index);
+  difference_type size = last - first;
+
+  while (index < size) {
+    // get the smallest (largest) child or grandchild
+    difference_type smallest = index;
+
+    difference_type i = mmheap_left_child(index);
+    difference_type end = std::min(i + 2, size);
+    for (; i < end; i++) {
+      if (comp(*(first + i), *(first + smallest)) ^ max_level) {
+        smallest = i;
+      }
+    }
+
+    i = mmheap_left_grandchild(index);
+    end = std::min(i + 4, size);
+    for (; i < end; i++) {
+      if (comp(*(first + i), *(first + smallest)) ^ max_level) {
+        smallest = i;
+      }
+    }
+
+    // already the smallest (largest) node, nothing to do
+    if (smallest == index) {
+      break;
+    }
+
+    // swap the node with the smallest (largest) descendant
+    std::swap(*(first + index), *(first + smallest));
+
+    // if the swapped node was a child, then the current node, its child, and
+    // its grandchild are all ordered correctly at this point satisfying the
+    // min-max order property
+    if (mmheap_is_child(index, smallest)) {
+      break;
+    }
+
+    // if the node's new parent is now smaller than it, swap again
+    if (comp(*(first + mmheap_parent(smallest)), *(first + smallest)) ^
+        max_level) {
+      std::swap(*(first + mmheap_parent(smallest)), *(first + smallest));
+    }
+
+    // if the swapped node was a grandchild, iteration must continue to
+    // ensure it's now ordered with regard to its descendants
+    index = smallest;
+  }
+}
+
+template <typename RandomIt, typename Comp>
+bool mmheap_validate(RandomIt first, RandomIt last, Comp comp) {
+  using difference_type =
+      typename std::iterator_traits<RandomIt>::difference_type;
+
+  difference_type size = last - first;
+
+  for (difference_type i = 0; i < size; i++) {
+    bool flip_compare = mmheap_is_max_level(i);
+
+    // values stored at nodes on even (odd) levels are smaller (greater) than
+    // or equal to the values stored at their descendants
+
+    // validate children
+    difference_type j = std::min(mmheap_left_child(i), size);
+    difference_type end = std::min(j + 2, size);
+
+    for (; j < end; j++) {
+      if (!(comp(*(first + i), *(first + j)) ^ flip_compare)) {
+        return false;
+      }
+    }
+
+    // validate grandchildren
+    j = std::min(mmheap_left_grandchild(i), size);
+    end = std::min(j + 4, size);
+
+    for (; j < end; j++) {
+      if (!(comp(*(first + i), *(first + j)) ^ flip_compare)) {
+        return false;
+      }
+    }
+  }
+
+  return true;
+}
+
+template <typename RandomIt>
+bool mmheap_validate(RandomIt first, RandomIt last) {
+  return mmheap_validate(
+      first, last,
+      std::less<typename std::iterator_traits<RandomIt>::value_type>());
+}
+
+template <typename RandomIt, typename Comp>
+void mmheap_push(RandomIt first, RandomIt last, Comp comp) {
+  mmheap_sift_up(first, last, comp, (last - first) - 1);
+}
+
+template <typename RandomIt>
+void mmheap_push(RandomIt first, RandomIt last) {
+  mmheap_push(first, last,
+              std::less<typename std::iterator_traits<RandomIt>::value_type>());
+}
+
+template <typename RandomIt, typename Comp>
+RandomIt mmheap_find_min(RandomIt first, RandomIt last, Comp comp) {
+  return first;
+}
+
+template <typename RandomIt>
+RandomIt mmheap_find_min(RandomIt first, RandomIt last) {
+  return mmheap_find_min(
+      first, last,
+      std::less<typename std::iterator_traits<RandomIt>::value_type>());
+}
+
+template <typename RandomIt, typename Comp>
+RandomIt mmheap_find_max(RandomIt first, RandomIt last, Comp comp) {
+  using difference_type =
+      typename std::iterator_traits<RandomIt>::difference_type;
+
+  difference_type size = last - first;
+
+  if (size == 1) {
+    // root must be the max
+    return first;
+  } else if (size == 2) {
+    // root's child must be the max
+    return first + 1;
+  } else {
+    // must be the larger of the two children
+    if (comp(*(first + 1), *(first + 2))) {
+      return first + 2;
+    } else {
+      return first + 1;
+    }
+  }
+}
+
+template <typename RandomIt>
+RandomIt mmheap_find_max(RandomIt first, RandomIt last) {
+  return mmheap_find_max(
+      first, last,
+      std::less<typename std::iterator_traits<RandomIt>::value_type>());
+}
+
+template <typename RandomIt, typename Comp>
+void mmheap_pop_min(RandomIt first, RandomIt last, Comp comp) {
+  if (first == last) {
+    return;
+  }
+
+  RandomIt min = mmheap_find_min(first, last, comp);
+  std::swap(*min, *--last);
+  mmheap_sift_down(first, last, comp, std::distance(first, min));
+}
+
+template <typename RandomIt>
+void mmheap_pop_min(RandomIt first, RandomIt last) {
+  mmheap_pop_min(
+      first, last,
+      std::less<typename std::iterator_traits<RandomIt>::value_type>());
+}
+
+template <typename RandomIt, typename Comp>
+void mmheap_pop_max(RandomIt first, RandomIt last, Comp comp) {
+  if (first == last) {
+    return;
+  }
+
+  RandomIt max = mmheap_find_max(first, last, comp);
+  std::swap(*max, *--last);
+  mmheap_sift_down(first, last, comp, std::distance(first, max));
+}
+
+template <typename RandomIt>
+void mmheap_pop_max(RandomIt first, RandomIt last) {
+  mmheap_pop_max(
+      first, last,
+      std::less<typename std::iterator_traits<RandomIt>::value_type>());
+}
+}
+
+#endif
diff --git a/src/core/ring_buffer.h b/src/core/ring_buffer.h
index b49fcab4..0028c752 100644
--- a/src/core/ring_buffer.h
+++ b/src/core/ring_buffer.h
@@ -122,24 +122,6 @@ class RingBuffer {
     front_++;
   }
 
-  void Insert(const iterator &it, const T &el) {
-    size_t end = front_ + max_ - 1;
-
-    // if the buffer isn't full, increase its size
-    if (back_ < end) {
-      end = back_++;
-    }
-
-    // shift old elements over by one
-    while ((end - front_) != it.index_) {
-      buffer_[end % max_] = buffer_[(end - 1) % max_];
-      end--;
-    }
-
-    // add new element
-    buffer_[end % max_] = el;
-  }
-
  private:
   T *buffer_;
   const size_t max_;
diff --git a/src/jit/ir/passes/register_allocation_pass.cc b/src/jit/ir/passes/register_allocation_pass.cc
index c3e771ce..807ec036 100644
--- a/src/jit/ir/passes/register_allocation_pass.cc
+++ b/src/jit/ir/passes/register_allocation_pass.cc
@@ -1,4 +1,5 @@
 #include "core/core.h"
+#include "core/minmax_heap.h"
 #include "emu/profiler.h"
 #include "jit/ir/passes/register_allocation_pass.h"
 
@@ -16,15 +17,25 @@ static inline bool RegisterCanStore(const Register &r, ValueTy type) {
   return r.value_types & (1 << type);
 }
 
-RegisterSet::RegisterSet(int max_registers) : live_(max_registers) {
+struct LiveIntervalSort {
+  bool operator()(const Interval *lhs, const Interval *rhs) const {
+    return GetOrdinal(lhs->next->instr()) < GetOrdinal(rhs->next->instr());
+  }
+};
+
+RegisterSet::RegisterSet(int max_registers) {
   free_ = new int[max_registers];
+  live_ = new Interval *[max_registers];
 }
 
-RegisterSet::~RegisterSet() { delete[] free_; }
+RegisterSet::~RegisterSet() {
+  delete[] free_;
+  delete[] live_;
+}
 
 void RegisterSet::Clear() {
   num_free_ = 0;
-  live_.Clear();
+  num_live_ = 0;
 }
 
 int RegisterSet::PopRegister() {
@@ -37,33 +48,36 @@ int RegisterSet::PopRegister() {
 void RegisterSet::PushRegister(int reg) { free_[num_free_++] = reg; }
 
 Interval *RegisterSet::HeadInterval() {
-  if (live_.Empty()) {
+  if (!num_live_) {
     return nullptr;
   }
 
-  return live_.front();
+  auto it = dvm::mmheap_find_min(live_, live_ + num_live_, LiveIntervalSort());
+  return *it;
 }
 
 Interval *RegisterSet::TailInterval() {
-  if (live_.Empty()) {
+  if (!num_live_) {
     return nullptr;
   }
 
-  return live_.back();
+  auto it = dvm::mmheap_find_max(live_, live_ + num_live_, LiveIntervalSort());
+  return *it;
 }
 
-void RegisterSet::PopHeadInterval() { live_.PopFront(); }
+void RegisterSet::PopHeadInterval() {
+  dvm::mmheap_pop_min(live_, live_ + num_live_, LiveIntervalSort());
+  num_live_--;
+}
 
-void RegisterSet::PopTailInterval() { live_.PopBack(); }
+void RegisterSet::PopTailInterval() {
+  dvm::mmheap_pop_max(live_, live_ + num_live_, LiveIntervalSort());
+  num_live_--;
+}
 
 void RegisterSet::InsertInterval(Interval *interval) {
-  auto it = std::lower_bound(live_.begin(), live_.end(),
-                             GetOrdinal(interval->next->instr()),
-                             [](const Interval *lhs, int rhs) {
-                               return GetOrdinal(lhs->next->instr()) < rhs;
-                             });
-
-  live_.Insert(it, interval);
+  live_[num_live_++] = interval;
+  dvm::mmheap_push(live_, live_ + num_live_, LiveIntervalSort());
 }
 
 RegisterAllocationPass::RegisterAllocationPass(const Backend &backend)
diff --git a/src/jit/ir/passes/register_allocation_pass.h b/src/jit/ir/passes/register_allocation_pass.h
index 66c2c7b6..2a0aff2f 100644
--- a/src/jit/ir/passes/register_allocation_pass.h
+++ b/src/jit/ir/passes/register_allocation_pass.h
@@ -1,7 +1,7 @@
 #ifndef REGISTER_ALLOCATION_PASS_H
 #define REGISTER_ALLOCATION_PASS_H
 
-#include "core/ring_buffer.h"
+#include <vector>
 #include "jit/backend/backend.h"
 #include "jit/ir/passes/pass_runner.h"
 
@@ -39,7 +39,8 @@ class RegisterSet {
   int *free_, num_free_;
 
   // intervals used by this register set, sorted in order of next use
-  RingBuffer<Interval *> live_;
+  Interval **live_;
+  int num_live_;
 };
 
 class RegisterAllocationPass : public Pass {
diff --git a/test/test_minmax_heap.cc b/test/test_minmax_heap.cc
new file mode 100644
index 00000000..73017065
--- /dev/null
+++ b/test/test_minmax_heap.cc
@@ -0,0 +1,117 @@
+#include <gtest/gtest.h>
+#include "core/minmax_heap.h"
+
+TEST(MinMaxHeap, PopEmpty) {
+  std::vector<int> elements;
+
+  // shouldn't do anything, just sanity checking that it doesn't crash
+  dvm::mmheap_pop_min(elements.begin(), elements.end());
+  ASSERT_TRUE(dvm::mmheap_validate(elements.begin(), elements.end()));
+
+  dvm::mmheap_pop_max(elements.begin(), elements.end());
+  ASSERT_TRUE(dvm::mmheap_validate(elements.begin(), elements.end()));
+}
+
+TEST(MinMaxHeap, PopMinRoot) {
+  std::vector<int> elements = {1};
+
+  dvm::mmheap_pop_min(elements.begin(), elements.end());
+  ASSERT_EQ(elements.back(), 1);
+  elements.pop_back();
+
+  ASSERT_TRUE(dvm::mmheap_validate(elements.begin(), elements.end()));
+}
+
+TEST(MinMaxHeap, PopMaxRoot) {
+  std::vector<int> elements = {1};
+
+  dvm::mmheap_pop_min(elements.begin(), elements.end());
+  ASSERT_EQ(elements.back(), 1);
+  elements.pop_back();
+
+  ASSERT_TRUE(dvm::mmheap_validate(elements.begin(), elements.end()));
+}
+
+TEST(MinMaxHeap, PopMax1) {
+  std::vector<int> elements = {1};
+
+  dvm::mmheap_pop_max(elements.begin(), elements.end());
+  ASSERT_EQ(elements.back(), 1);
+  elements.pop_back();
+
+  ASSERT_TRUE(dvm::mmheap_validate(elements.begin(), elements.end()));
+}
+
+TEST(MinMaxHeap, PopMax2) {
+  std::vector<int> elements = {1, 2};
+
+  dvm::mmheap_pop_max(elements.begin(), elements.end());
+  ASSERT_EQ(elements.back(), 2);
+  elements.pop_back();
+
+  ASSERT_TRUE(dvm::mmheap_validate(elements.begin(), elements.end()));
+}
+
+TEST(MinMaxHeap, PopMax3) {
+  {
+    std::vector<int> elements = {1, 2, 3};
+
+    dvm::mmheap_pop_max(elements.begin(), elements.end());
+    ASSERT_EQ(elements.back(), 3);
+    elements.pop_back();
+
+    ASSERT_TRUE(dvm::mmheap_validate(elements.begin(), elements.end()));
+  }
+
+  {
+    std::vector<int> elements = {1, 3, 2};
+
+    dvm::mmheap_pop_max(elements.begin(), elements.end());
+    ASSERT_EQ(elements.back(), 3);
+    elements.pop_back();
+
+    ASSERT_TRUE(dvm::mmheap_validate(elements.begin(), elements.end()));
+  }
+}
+
+TEST(MinMaxHeap, PushPopMinN) {
+  static const int N = 1337;
+
+  std::vector<int> elements = {};
+
+  for (int i = 0; i < N; i++) {
+    elements.push_back(i);
+    dvm::mmheap_push(elements.begin(), elements.end());
+
+    ASSERT_TRUE(dvm::mmheap_validate(elements.begin(), elements.end()));
+  }
+
+  for (int i = 0; i < N; i++) {
+    dvm::mmheap_pop_min(elements.begin(), elements.end());
+    ASSERT_EQ(elements.back(), i);
+    elements.pop_back();
+
+    ASSERT_TRUE(dvm::mmheap_validate(elements.begin(), elements.end()));
+  }
+}
+
+TEST(MinMaxHeap, PushPopMaxN) {
+  static const int N = 1337;
+
+  std::vector<int> elements = {};
+
+  for (int i = 0; i < N; i++) {
+    elements.push_back(i);
+    dvm::mmheap_push(elements.begin(), elements.end());
+
+    ASSERT_TRUE(dvm::mmheap_validate(elements.begin(), elements.end()));
+  }
+
+  for (int i = N - 1; i >= 0; i--) {
+    dvm::mmheap_pop_max(elements.begin(), elements.end());
+    ASSERT_EQ(elements.back(), i);
+    elements.pop_back();
+
+    ASSERT_TRUE(dvm::mmheap_validate(elements.begin(), elements.end()));
+  }
+}
diff --git a/test/test_ring_buffer.cc b/test/test_ring_buffer.cc
index b5dd3189..67f67f1b 100644
--- a/test/test_ring_buffer.cc
+++ b/test/test_ring_buffer.cc
@@ -47,27 +47,6 @@ TEST_F(RingTest, PushBack) {
   ASSERT_EQ(2, (int)items.Size());
 }
 
-TEST_F(RingTest, Insert) {
-  items.PushBack(7);
-  items.PushBack(9);
-
-  // insert at beginning
-  items.Insert(items.begin(), 3);
-  ASSERT_EQ(3, items.front());
-  ASSERT_EQ(3, *items.begin());
-  ASSERT_EQ(7, items.back());
-  ASSERT_EQ(7, *(--items.end()));
-  ASSERT_EQ(2, (int)items.Size());
-
-  // insert at end
-  items.Insert(++items.begin(), 5);
-  ASSERT_EQ(3, items.front());
-  ASSERT_EQ(3, *items.begin());
-  ASSERT_EQ(5, items.back());
-  ASSERT_EQ(5, *(--items.end()));
-  ASSERT_EQ(2, (int)items.Size());
-}
-
 // remove tests
 TEST_F(RingTest, PopBack) {
   items.PushBack(7);