diff --git a/llvm/lib/Analysis/BasicAliasAnalysis.cpp b/llvm/lib/Analysis/BasicAliasAnalysis.cpp
--- a/llvm/lib/Analysis/BasicAliasAnalysis.cpp
+++ b/llvm/lib/Analysis/BasicAliasAnalysis.cpp
@@ -1288,8 +1288,12 @@
     if (V1Size.hasValue() && V2Size.hasValue()) {
       // Try to determine whether abs(VarIndex) > 0.
       Optional<APInt> MinAbsVarIndex;
-      // TODO: Could handle single non-zero index as well.
-      if (DecompGEP1.VarIndices.size() == 2) {
+      if (DecompGEP1.VarIndices.size() == 1) {
+        // VarIndex = Scale*V. If V != 0 then abs(VarIndex) >= abs(Scale).
+        const VariableGEPIndex &Var = DecompGEP1.VarIndices[0];
+        if (isKnownNonZero(Var.V, DL))
+          MinAbsVarIndex = Var.Scale.abs();
+      } else if (DecompGEP1.VarIndices.size() == 2) {
         // VarIndex = Scale*V0 + (-Scale)*V1.
         // If V0 != V1 then abs(VarIndex) >= abs(Scale).
         // Check that VisitedPhiBBs is empty, to avoid reasoning about
diff --git a/llvm/test/Analysis/BasicAA/bug.23626.ll b/llvm/test/Analysis/BasicAA/bug.23626.ll
--- a/llvm/test/Analysis/BasicAA/bug.23626.ll
+++ b/llvm/test/Analysis/BasicAA/bug.23626.ll
@@ -4,9 +4,9 @@
 
 ; CHECK-LABEL: compute1
 ; CHECK: MayAlias:	i32* %arrayidx8, i32* %out
-; CHECK: MayAlias:	i32* %arrayidx11, i32* %out
+; CHECK: NoAlias:	i32* %arrayidx11, i32* %out
 ; CHECK: MayAlias:	i32* %arrayidx11, i32* %arrayidx8
-; CHECK: MayAlias:	i32* %arrayidx14, i32* %out
+; CHECK: NoAlias:	i32* %arrayidx14, i32* %out
 ; CHECK: MayAlias:	i32* %arrayidx14, i32* %arrayidx8
 ; CHECK: MayAlias:	i32* %arrayidx11, i32* %arrayidx14
 define void @compute1(i32 %num.0.lcssa, i32* %out) {
diff --git a/llvm/test/Analysis/BasicAA/sequential-gep.ll b/llvm/test/Analysis/BasicAA/sequential-gep.ll
--- a/llvm/test/Analysis/BasicAA/sequential-gep.ll
+++ b/llvm/test/Analysis/BasicAA/sequential-gep.ll
@@ -111,10 +111,9 @@
 }
 
 ; CHECK-LABEL: non_zero_index_simple
-; CHECK: MayAlias: i32* %gep, i32* %p
-; CHECK: MayAlias: i16* %gep.16, i32* %p
+; CHECK: NoAlias: i32* %gep, i32* %p
+; CHECK: NoAlias: i16* %gep.16, i32* %p
 ; CHECK: MayAlias: i32* %p, i64* %gep.64
-; TODO: First two could be NoAlias.
 define void @non_zero_index_simple(i32* %p, i32* %q) {
   %knownnonzero = load i32, i32* %q, !range !0
   %gep = getelementptr i32, i32* %p, i32 %knownnonzero
@@ -125,8 +124,7 @@
 
 ; CHECK-LABEL: non_zero_index_with_offset
 ; CHECK: MayAlias: i32* %gep, i32* %p
-; CHECK: MayAlias: i16* %gep.16, i32* %p
-; TODO: Last could be NoAlias.
+; CHECK: NoAlias: i16* %gep.16, i32* %p
 define void @non_zero_index_with_offset(i32* %p, i32* %q) {
   %knownnonzero = load i32, i32* %q, !range !0
   %p.8 = bitcast i32* %p to i8*