diff --git a/llvm/include/llvm/CodeGen/TargetRegisterInfo.h b/llvm/include/llvm/CodeGen/TargetRegisterInfo.h
--- a/llvm/include/llvm/CodeGen/TargetRegisterInfo.h
+++ b/llvm/include/llvm/CodeGen/TargetRegisterInfo.h
@@ -55,6 +55,8 @@
   const LaneBitmask LaneMask;
   /// Classes with a higher priority value are assigned first by register
   /// allocators using a greedy heuristic. The value is in the range [0,63].
+  /// Values >= 32 should be used with care since they may overlap with other
+  /// fields in the allocator's priority heuristics.
   const uint8_t AllocationPriority;
   /// Configurable target specific flags.
   const uint8_t TSFlags;
@@ -1076,6 +1078,14 @@
     return false;
   }
 
+  /// When prioritizing live ranges in register allocation, if this hook returns
+  /// true then the AllocationPriority of the register class will be treated as
+  /// more important than whether the range is local to a basic block or global.
+  virtual bool
+  regClassPriorityTrumpsGlobalness(const MachineFunction &MF) const {
+    return false;
+  }
+
   //===--------------------------------------------------------------------===//
   /// Debug information queries.
 
diff --git a/llvm/include/llvm/Target/Target.td b/llvm/include/llvm/Target/Target.td
--- a/llvm/include/llvm/Target/Target.td
+++ b/llvm/include/llvm/Target/Target.td
@@ -279,6 +279,8 @@
   // heuristic. Classes with higher priority values are assigned first. This is
   // useful as it is sometimes beneficial to assign registers to highly
   // constrained classes first. The value has to be in the range [0,63].
+  // Values >= 32 should be used with care since they may overlap with other
+  // fields in the allocator's priority heuristics.
   int AllocationPriority = 0;
 
   // Generate register pressure set for this register class and any class
diff --git a/llvm/lib/CodeGen/RegAllocGreedy.h b/llvm/lib/CodeGen/RegAllocGreedy.h
--- a/llvm/lib/CodeGen/RegAllocGreedy.h
+++ b/llvm/lib/CodeGen/RegAllocGreedy.h
@@ -322,6 +322,10 @@
   /// Function
   ArrayRef<uint8_t> RegCosts;
 
+  /// Flags for the live range priority calculation, determined once per
+  /// machine function.
+  bool RegClassPriorityTrumpsGlobalness;
+
 public:
   RAGreedy(const RegClassFilterFunc F = allocateAllRegClasses);
 
diff --git a/llvm/lib/CodeGen/RegAllocGreedy.cpp b/llvm/lib/CodeGen/RegAllocGreedy.cpp
--- a/llvm/lib/CodeGen/RegAllocGreedy.cpp
+++ b/llvm/lib/CodeGen/RegAllocGreedy.cpp
@@ -128,6 +128,13 @@
              "limit its budget and bail out once we reach the limit."),
     cl::init(10000), cl::Hidden);
 
+static cl::opt<bool> GreedyRegClassPriorityTrumpsGlobalness(
+    "greedy-regclass-priority-trumps-globalness",
+    cl::desc("Change the greedy register allocator's live range priority "
+             "calculation to make the AllocationPriority of the register class "
+             "more important then whether the range is global"),
+    cl::Hidden);
+
 static RegisterRegAlloc greedyRegAlloc("greedy", "greedy register allocator",
                                        createGreedyRegisterAllocator);
 
@@ -305,6 +312,7 @@
     const TargetRegisterClass &RC = *MRI->getRegClass(Reg);
     bool ForceGlobal = !ReverseLocal &&
       (Size / SlotIndex::InstrDist) > (2 * RCI.getNumAllocatableRegs(&RC));
+    unsigned GlobalBit = 0;
 
     if (Stage == RS_Assign && !ForceGlobal && !LI->empty() &&
         LIS->intervalIsInOneMBB(*LI)) {
@@ -323,9 +331,13 @@
       // Allocate global and split ranges in long->short order. Long ranges that
       // don't fit should be spilled (or split) ASAP so they don't create
       // interference.  Mark a bit to prioritize global above local ranges.
-      Prio = (1u << 29) + Size;
+      Prio = Size;
+      GlobalBit = 1;
     }
-    Prio |= RC.AllocationPriority << 24;
+    if (RegClassPriorityTrumpsGlobalness)
+      Prio |= RC.AllocationPriority << 25 | GlobalBit << 24;
+    else
+      Prio |= GlobalBit << 29 | RC.AllocationPriority << 24;
 
     // Mark a higher bit to prioritize global and local above RS_Split.
     Prio |= (1u << 31);
@@ -2692,6 +2704,10 @@
   initializeCSRCost();
 
   RegCosts = TRI->getRegisterCosts(*MF);
+  RegClassPriorityTrumpsGlobalness =
+      GreedyRegClassPriorityTrumpsGlobalness.getNumOccurrences()
+          ? GreedyRegClassPriorityTrumpsGlobalness
+          : TRI->regClassPriorityTrumpsGlobalness(*MF);
 
   ExtraInfo.emplace();
   EvictAdvisor =
diff --git a/llvm/test/CodeGen/AMDGPU/greedy-liverange-priority.mir b/llvm/test/CodeGen/AMDGPU/greedy-liverange-priority.mir
new file mode 100644
--- /dev/null
+++ b/llvm/test/CodeGen/AMDGPU/greedy-liverange-priority.mir
@@ -0,0 +1,48 @@
+# RUN: llc -march=amdgcn -mcpu=gfx1030 -greedy-regclass-priority-trumps-globalness=0 -start-before greedy -o - %s | FileCheck %s -check-prefix=OLD
+# RUN: llc -march=amdgcn -mcpu=gfx1030 -greedy-regclass-priority-trumps-globalness=1 -start-before greedy -o - %s | FileCheck %s -check-prefix=NEW
+
+# At the time of writing -greedy-regclass-priority-trumps-globalness makes a
+# significant improvement in the total number of vgprs needed to compile this
+# test, from 11 down to 7.
+
+# OLD: NumVgprs: 11{{$}}
+# NEW: NumVgprs: 7{{$}}
+
+---
+name: _amdgpu_cs_main
+tracksRegLiveness: true
+body: |
+  bb.0:
+    successors: %bb.1, %bb.2
+    liveins: $vgpr0, $vgpr6
+
+    %6:vgpr_32 = COPY $vgpr6
+    undef %30.sub0:vreg_128 = COPY $vgpr0
+    undef %27.sub0:vreg_128 = V_MED3_F32_e64 0, 0, 0, 0, 0, 0, 0, 0, implicit $mode, implicit $exec
+    undef %16.sub0:sgpr_256 = S_MOV_B32 0
+    undef %26.sub1:vreg_64 = V_LSHRREV_B32_e32 1, %6, implicit $exec
+    %27.sub1:vreg_128 = COPY %27.sub0
+    %27.sub2:vreg_128 = COPY %27.sub0
+    %27.sub3:vreg_128 = COPY %27.sub0
+    %26.sub0:vreg_64 = V_MOV_B32_e32 1, implicit $exec
+    %16.sub1:sgpr_256 = COPY %16.sub0
+    %16.sub2:sgpr_256 = COPY %16.sub0
+    %16.sub3:sgpr_256 = COPY %16.sub0
+    %16.sub4:sgpr_256 = COPY %16.sub0
+    %16.sub5:sgpr_256 = COPY %16.sub0
+    %16.sub6:sgpr_256 = COPY %16.sub0
+    %16.sub7:sgpr_256 = COPY %16.sub0
+    IMAGE_STORE_V4_V2_gfx10 %27, %26, %16, 0, 1, -1, 0, 0, 0, 0, 0, 0, implicit $exec :: (dereferenceable store (s32) into custom "ImageResource")
+    S_CBRANCH_SCC1 %bb.2, implicit undef $scc
+    S_BRANCH %bb.1
+
+  bb.1:
+    %30.sub1:vreg_128 = V_MOV_B32_e32 0, implicit $exec
+    %30.sub2:vreg_128 = COPY %30.sub1
+    %30.sub3:vreg_128 = COPY %30.sub1
+    %26.sub1:vreg_64 = COPY %30.sub1
+    IMAGE_STORE_V4_V2_gfx10 %30, %26, %16, 0, 1, -1, 0, 0, 0, 0, 0, 0, implicit $exec :: (dereferenceable store (s32) into custom "ImageResource")
+
+  bb.2:
+    S_ENDPGM 0
+...