diff --git a/llvm/lib/Target/SystemZ/SystemZ.h b/llvm/lib/Target/SystemZ/SystemZ.h
index 051ba1dcfb66..1647d93c02dc 100644
--- a/llvm/lib/Target/SystemZ/SystemZ.h
+++ b/llvm/lib/Target/SystemZ/SystemZ.h
@@ -62,6 +62,10 @@ namespace llvm {
     const unsigned CCMASK_TM_MIXED_MSB_0 = CCMASK_1;
     const unsigned CCMASK_TM_MIXED_MSB_1 = CCMASK_2;
     const unsigned CCMASK_TM_ALL_1       = CCMASK_3;
+    const unsigned CCMASK_TM_SOME_0      = CCMASK_TM_ALL_1 ^ CCMASK_ANY;
+    const unsigned CCMASK_TM_SOME_1      = CCMASK_TM_ALL_0 ^ CCMASK_ANY;
+    const unsigned CCMASK_TM_MSB_0       = CCMASK_0 | CCMASK_1;
+    const unsigned CCMASK_TM_MSB_1       = CCMASK_2 | CCMASK_3;
     const unsigned CCMASK_TM             = CCMASK_ANY;
 
     // Mask assignments for PFD.
diff --git a/llvm/lib/Target/SystemZ/SystemZISelLowering.cpp b/llvm/lib/Target/SystemZ/SystemZISelLowering.cpp
index 1ab1ef4acaf3..13d5604be13d 100644
--- a/llvm/lib/Target/SystemZ/SystemZISelLowering.cpp
+++ b/llvm/lib/Target/SystemZ/SystemZISelLowering.cpp
@@ -1176,6 +1176,98 @@ static bool shouldSwapCmpOperands(SDValue Op0, SDValue Op1,
   return false;
 }
 
+// Check whether the CC value produced by TEST UNDER MASK is descriptive
+// enough to handle an AND with Mask followed by a comparison of type Opcode
+// with CmpVal.  CCMask says which comparison result is being tested and
+// BitSize is the number of bits in the operands.  Return the CC mask that
+// should be used for the TEST UNDER MASK result, or 0 if the condition is
+// too complex.
+static unsigned getTestUnderMaskCond(unsigned BitSize, unsigned Opcode,
+                                     unsigned CCMask, uint64_t Mask,
+                                     uint64_t CmpVal) {
+  assert(Mask != 0 && "ANDs with zero should have been removed by now");
+
+  // Work out the masks for the lowest and highest bits.
+  unsigned HighShift = 63 - countLeadingZeros(Mask);
+  uint64_t High = uint64_t(1) << HighShift;
+  uint64_t Low = uint64_t(1) << countTrailingZeros(Mask);
+
+  // Signed ordered comparisons are effectively unsigned if the sign
+  // bit is dropped.
+  bool EffectivelyUnsigned = (Opcode == SystemZISD::UCMP
+                              || HighShift < BitSize - 1);
+
+  // Check for equality comparisons with 0, or the equivalent.
+  if (CmpVal == 0) {
+    if (CCMask == SystemZ::CCMASK_CMP_EQ)
+      return SystemZ::CCMASK_TM_ALL_0;
+    if (CCMask == SystemZ::CCMASK_CMP_NE)
+      return SystemZ::CCMASK_TM_SOME_1;
+  }
+  if (EffectivelyUnsigned && CmpVal <= Low) {
+    if (CCMask == SystemZ::CCMASK_CMP_LT)
+      return SystemZ::CCMASK_TM_ALL_0;
+    if (CCMask == SystemZ::CCMASK_CMP_GE)
+      return SystemZ::CCMASK_TM_SOME_1;
+  }
+  if (EffectivelyUnsigned && CmpVal < Low) {
+    if (CCMask == SystemZ::CCMASK_CMP_LE)
+      return SystemZ::CCMASK_TM_ALL_0;
+    if (CCMask == SystemZ::CCMASK_CMP_GT)
+      return SystemZ::CCMASK_TM_SOME_1;
+  }
+
+  // Check for equality comparisons with the mask, or the equivalent.
+  if (CmpVal == Mask) {
+    if (CCMask == SystemZ::CCMASK_CMP_EQ)
+      return SystemZ::CCMASK_TM_ALL_1;
+    if (CCMask == SystemZ::CCMASK_CMP_NE)
+      return SystemZ::CCMASK_TM_SOME_0;
+  }
+  if (EffectivelyUnsigned && CmpVal >= Mask - Low && CmpVal < Mask) {
+    if (CCMask == SystemZ::CCMASK_CMP_GT)
+      return SystemZ::CCMASK_TM_ALL_1;
+    if (CCMask == SystemZ::CCMASK_CMP_LE)
+      return SystemZ::CCMASK_TM_SOME_0;
+  }
+  if (EffectivelyUnsigned && CmpVal > Mask - Low && CmpVal <= Mask) {
+    if (CCMask == SystemZ::CCMASK_CMP_GE)
+      return SystemZ::CCMASK_TM_ALL_1;
+    if (CCMask == SystemZ::CCMASK_CMP_LT)
+      return SystemZ::CCMASK_TM_SOME_0;
+  }
+
+  // Check for ordered comparisons with the top bit.
+  if (EffectivelyUnsigned && CmpVal >= Mask - High && CmpVal < High) {
+    if (CCMask == SystemZ::CCMASK_CMP_LE)
+      return SystemZ::CCMASK_TM_MSB_0;
+    if (CCMask == SystemZ::CCMASK_CMP_GT)
+      return SystemZ::CCMASK_TM_MSB_1;
+  }
+  if (EffectivelyUnsigned && CmpVal > Mask - High && CmpVal <= High) {
+    if (CCMask == SystemZ::CCMASK_CMP_LT)
+      return SystemZ::CCMASK_TM_MSB_0;
+    if (CCMask == SystemZ::CCMASK_CMP_GE)
+      return SystemZ::CCMASK_TM_MSB_1;
+  }
+
+  // If there are just two bits, we can do equality checks for Low and High
+  // as well.
+  if (Mask == Low + High) {
+    if (CCMask == SystemZ::CCMASK_CMP_EQ && CmpVal == Low)
+      return SystemZ::CCMASK_TM_MIXED_MSB_0;
+    if (CCMask == SystemZ::CCMASK_CMP_NE && CmpVal == Low)
+      return SystemZ::CCMASK_TM_MIXED_MSB_0 ^ SystemZ::CCMASK_ANY;
+    if (CCMask == SystemZ::CCMASK_CMP_EQ && CmpVal == High)
+      return SystemZ::CCMASK_TM_MIXED_MSB_1;
+    if (CCMask == SystemZ::CCMASK_CMP_NE && CmpVal == High)
+      return SystemZ::CCMASK_TM_MIXED_MSB_1 ^ SystemZ::CCMASK_ANY;
+  }
+
+  // Looks like we've exhausted our options.
+  return 0;
+}
+
 // See whether the comparison (Opcode CmpOp0, CmpOp1) can be implemented
 // as a TEST UNDER MASK instruction when the condition being tested is
 // as described by CCValid and CCMask.  Update the arguments with the
@@ -1183,12 +1275,9 @@ static bool shouldSwapCmpOperands(SDValue Op0, SDValue Op1,
 static void adjustForTestUnderMask(unsigned &Opcode, SDValue &CmpOp0,
                                    SDValue &CmpOp1, unsigned &CCValid,
                                    unsigned &CCMask) {
-  // For now we just handle equality and inequality with zero.
-  if (CCMask != SystemZ::CCMASK_CMP_EQ &&
-      (CCMask ^ CCValid) != SystemZ::CCMASK_CMP_EQ)
-    return;
+  // Check that we have a comparison with a constant.
   ConstantSDNode *ConstCmpOp1 = dyn_cast<ConstantSDNode>(CmpOp1);
-  if (!ConstCmpOp1 || ConstCmpOp1->getZExtValue() != 0)
+  if (!ConstCmpOp1)
     return;
 
   // Check whether the nonconstant input is an AND with a constant mask.
@@ -1206,14 +1295,20 @@ static void adjustForTestUnderMask(unsigned &Opcode, SDValue &CmpOp0,
       !SystemZ::isImmHL(MaskVal) && !SystemZ::isImmHH(MaskVal))
     return;
 
+  // Check whether the combination of mask, comparison value and comparison
+  // type are suitable.
+  unsigned BitSize = CmpOp0.getValueType().getSizeInBits();
+  unsigned NewCCMask = getTestUnderMaskCond(BitSize, Opcode, CCMask, MaskVal,
+                                            ConstCmpOp1->getZExtValue());
+  if (!NewCCMask)
+    return;
+
   // Go ahead and make the change.
   Opcode = SystemZISD::TM;
   CmpOp0 = AndOp0;
   CmpOp1 = AndOp1;
   CCValid = SystemZ::CCMASK_TM;
-  CCMask = (CCMask == SystemZ::CCMASK_CMP_EQ ?
-            SystemZ::CCMASK_TM_ALL_0 :
-            SystemZ::CCMASK_TM_ALL_0 ^ CCValid);
+  CCMask = NewCCMask;
 }
 
 // Return a target node that compares CmpOp0 with CmpOp1 and stores a
diff --git a/llvm/test/CodeGen/SystemZ/int-cmp-46.ll b/llvm/test/CodeGen/SystemZ/int-cmp-46.ll
index b46ca5e6d1f5..339ba11694a4 100644
--- a/llvm/test/CodeGen/SystemZ/int-cmp-46.ll
+++ b/llvm/test/CodeGen/SystemZ/int-cmp-46.ll
@@ -97,3 +97,355 @@ store:
 exit:
   ret void
 }
+
+; Check that we can use TMLL for LT comparisons that are equivalent to
+; an equality comparison with zero.
+define void @f6(i32 %a) {
+; CHECK-LABEL: f6:
+; CHECK: tmll %r2, 240
+; CHECK: je {{\.L.*}}
+; CHECK: br %r14
+entry:
+  %and = and i32 %a, 240
+  %cmp = icmp slt i32 %and, 16
+  br i1 %cmp, label %exit, label %store
+
+store:
+  store i32 1, i32 *@g
+  br label %exit
+
+exit:
+  ret void
+}
+
+; ...same again with LE.
+define void @f7(i32 %a) {
+; CHECK-LABEL: f7:
+; CHECK: tmll %r2, 240
+; CHECK: je {{\.L.*}}
+; CHECK: br %r14
+entry:
+  %and = and i32 %a, 240
+  %cmp = icmp sle i32 %and, 15
+  br i1 %cmp, label %exit, label %store
+
+store:
+  store i32 1, i32 *@g
+  br label %exit
+
+exit:
+  ret void
+}
+
+; Check that we can use TMLL for GE comparisons that are equivalent to
+; an inequality comparison with zero.
+define void @f8(i32 %a) {
+; CHECK-LABEL: f8:
+; CHECK: tmll %r2, 240
+; CHECK: jne {{\.L.*}}
+; CHECK: br %r14
+entry:
+  %and = and i32 %a, 240
+  %cmp = icmp uge i32 %and, 16
+  br i1 %cmp, label %exit, label %store
+
+store:
+  store i32 1, i32 *@g
+  br label %exit
+
+exit:
+  ret void
+}
+
+; ...same again with GT.
+define void @f9(i32 %a) {
+; CHECK-LABEL: f9:
+; CHECK: tmll %r2, 240
+; CHECK: jne {{\.L.*}}
+; CHECK: br %r14
+entry:
+  %and = and i32 %a, 240
+  %cmp = icmp ugt i32 %and, 15
+  br i1 %cmp, label %exit, label %store
+
+store:
+  store i32 1, i32 *@g
+  br label %exit
+
+exit:
+  ret void
+}
+
+; Check that we can use TMLL for LT comparisons that effectively
+; test whether the top bit is clear.
+define void @f10(i32 %a) {
+; CHECK-LABEL: f10:
+; CHECK: tmll %r2, 35
+; CHECK: jle {{\.L.*}}
+; CHECK: br %r14
+entry:
+  %and = and i32 %a, 35
+  %cmp = icmp ult i32 %and, 8
+  br i1 %cmp, label %exit, label %store
+
+store:
+  store i32 1, i32 *@g
+  br label %exit
+
+exit:
+  ret void
+}
+
+; ...same again with LE.
+define void @f11(i32 %a) {
+; CHECK-LABEL: f11:
+; CHECK: tmll %r2, 35
+; CHECK: jle {{\.L.*}}
+; CHECK: br %r14
+entry:
+  %and = and i32 %a, 35
+  %cmp = icmp ule i32 %and, 31
+  br i1 %cmp, label %exit, label %store
+
+store:
+  store i32 1, i32 *@g
+  br label %exit
+
+exit:
+  ret void
+}
+
+; Check that we can use TMLL for GE comparisons that effectively test
+; whether the top bit is set.
+define void @f12(i32 %a) {
+; CHECK-LABEL: f12:
+; CHECK: tmll %r2, 140
+; CHECK: jnle {{\.L.*}}
+; CHECK: br %r14
+entry:
+  %and = and i32 %a, 140
+  %cmp = icmp uge i32 %and, 128
+  br i1 %cmp, label %exit, label %store
+
+store:
+  store i32 1, i32 *@g
+  br label %exit
+
+exit:
+  ret void
+}
+
+; ...same again for GT.
+define void @f13(i32 %a) {
+; CHECK-LABEL: f13:
+; CHECK: tmll %r2, 140
+; CHECK: jnle {{\.L.*}}
+; CHECK: br %r14
+entry:
+  %and = and i32 %a, 140
+  %cmp = icmp ugt i32 %and, 126
+  br i1 %cmp, label %exit, label %store
+
+store:
+  store i32 1, i32 *@g
+  br label %exit
+
+exit:
+  ret void
+}
+
+; Check that we can use TMLL for equality comparisons with the mask.
+define void @f14(i32 %a) {
+; CHECK-LABEL: f14:
+; CHECK: tmll %r2, 101
+; CHECK: jo {{\.L.*}}
+; CHECK: br %r14
+entry:
+  %and = and i32 %a, 101
+  %cmp = icmp eq i32 %and, 101
+  br i1 %cmp, label %exit, label %store
+
+store:
+  store i32 1, i32 *@g
+  br label %exit
+
+exit:
+  ret void
+}
+
+; Check that we can use TMLL for inequality comparisons with the mask.
+define void @f15(i32 %a) {
+; CHECK-LABEL: f15:
+; CHECK: tmll %r2, 65519
+; CHECK: jno {{\.L.*}}
+; CHECK: br %r14
+entry:
+  %and = and i32 %a, 65519
+  %cmp = icmp ne i32 %and, 65519
+  br i1 %cmp, label %exit, label %store
+
+store:
+  store i32 1, i32 *@g
+  br label %exit
+
+exit:
+  ret void
+}
+
+; Check that we can use TMLL for LT comparisons that are equivalent
+; to inequality comparisons with the mask.
+define void @f16(i32 %a) {
+; CHECK-LABEL: f16:
+; CHECK: tmll %r2, 130
+; CHECK: jno {{\.L.*}}
+; CHECK: br %r14
+entry:
+  %and = and i32 %a, 130
+  %cmp = icmp ult i32 %and, 129
+  br i1 %cmp, label %exit, label %store
+
+store:
+  store i32 1, i32 *@g
+  br label %exit
+
+exit:
+  ret void
+}
+
+; ...same again with LE.
+define void @f17(i32 %a) {
+; CHECK-LABEL: f17:
+; CHECK: tmll %r2, 130
+; CHECK: jno {{\.L.*}}
+; CHECK: br %r14
+entry:
+  %and = and i32 %a, 130
+  %cmp = icmp ule i32 %and, 128
+  br i1 %cmp, label %exit, label %store
+
+store:
+  store i32 1, i32 *@g
+  br label %exit
+
+exit:
+  ret void
+}
+
+; Check that we can use TMLL for GE comparisons that are equivalent
+; to equality comparisons with the mask.
+define void @f18(i32 %a) {
+; CHECK-LABEL: f18:
+; CHECK: tmll %r2, 194
+; CHECK: jo {{\.L.*}}
+; CHECK: br %r14
+entry:
+  %and = and i32 %a, 194
+  %cmp = icmp uge i32 %and, 193
+  br i1 %cmp, label %exit, label %store
+
+store:
+  store i32 1, i32 *@g
+  br label %exit
+
+exit:
+  ret void
+}
+
+; ...same again for GT.
+define void @f19(i32 %a) {
+; CHECK-LABEL: f19:
+; CHECK: tmll %r2, 194
+; CHECK: jo {{\.L.*}}
+; CHECK: br %r14
+entry:
+  %and = and i32 %a, 194
+  %cmp = icmp ugt i32 %and, 192
+  br i1 %cmp, label %exit, label %store
+
+store:
+  store i32 1, i32 *@g
+  br label %exit
+
+exit:
+  ret void
+}
+
+; Check that we can use TMLL for equality comparisons for the low bit
+; when the mask has two bits.
+define void @f20(i32 %a) {
+; CHECK-LABEL: f20:
+; CHECK: tmll %r2, 20
+; CHECK: jl {{\.L.*}}
+; CHECK: br %r14
+entry:
+  %and = and i32 %a, 20
+  %cmp = icmp eq i32 %and, 4
+  br i1 %cmp, label %exit, label %store
+
+store:
+  store i32 1, i32 *@g
+  br label %exit
+
+exit:
+  ret void
+}
+
+; Check that we can use TMLL for inequality comparisons for the low bit
+; when the mask has two bits.
+define void @f21(i32 %a) {
+; CHECK-LABEL: f21:
+; CHECK: tmll %r2, 20
+; CHECK: jnl {{\.L.*}}
+; CHECK: br %r14
+entry:
+  %and = and i32 %a, 20
+  %cmp = icmp ne i32 %and, 4
+  br i1 %cmp, label %exit, label %store
+
+store:
+  store i32 1, i32 *@g
+  br label %exit
+
+exit:
+  ret void
+}
+
+; Check that we can use TMLL for equality comparisons for the high bit
+; when the mask has two bits.
+define void @f22(i32 %a) {
+; CHECK-LABEL: f22:
+; CHECK: tmll %r2, 20
+; CHECK: jh {{\.L.*}}
+; CHECK: br %r14
+entry:
+  %and = and i32 %a, 20
+  %cmp = icmp eq i32 %and, 16
+  br i1 %cmp, label %exit, label %store
+
+store:
+  store i32 1, i32 *@g
+  br label %exit
+
+exit:
+  ret void
+}
+
+; Check that we can use TMLL for inequality comparisons for the high bit
+; when the mask has two bits.
+define void @f23(i32 %a) {
+; CHECK-LABEL: f23:
+; CHECK: tmll %r2, 20
+; CHECK: jnh {{\.L.*}}
+; CHECK: br %r14
+entry:
+  %and = and i32 %a, 20
+  %cmp = icmp ne i32 %and, 16
+  br i1 %cmp, label %exit, label %store
+
+store:
+  store i32 1, i32 *@g
+  br label %exit
+
+exit:
+  ret void
+}