diff --git a/llvm/lib/Transforms/Utils/SimplifyCFG.cpp b/llvm/lib/Transforms/Utils/SimplifyCFG.cpp
--- a/llvm/lib/Transforms/Utils/SimplifyCFG.cpp
+++ b/llvm/lib/Transforms/Utils/SimplifyCFG.cpp
@@ -3145,6 +3145,12 @@
       DTU->applyUpdates(Updates);
     }
 
+    // For simplicity, we created a separate basic block for the edge. Merge
+    // it back into the predecessor if possible. This not only avoids
+    // unnecessary SimplifyCFG iterations, but also makes sure that we don't
+    // bypass the check for trivial cycles above.
+    MergeBlockIntoPredecessor(EdgeBB, DTU);
+
     // Signal repeat, simplifying any other constants.
     return None;
   }
diff --git a/llvm/test/Transforms/SimplifyCFG/pr55765.ll b/llvm/test/Transforms/SimplifyCFG/pr55765.ll
new file mode 100644
--- /dev/null
+++ b/llvm/test/Transforms/SimplifyCFG/pr55765.ll
@@ -0,0 +1,63 @@
+; NOTE: Assertions have been autogenerated by utils/update_test_checks.py
+; RUN: opt -S -simplifycfg < %s | FileCheck %s
+
+; This used to infinitely thread between loop and loop.latch without reaching a
+; fixed point.
+
+declare void @dummy()
+
+define i32 @main(i1 %c1, i1 %c2, i32 %y) {
+; CHECK-LABEL: @main(
+; CHECK-NEXT:    br i1 [[C1:%.*]], label [[EXIT:%.*]], label [[LOOP_PRE_PREHEADER:%.*]]
+; CHECK:       loop.pre.preheader:
+; CHECK-NEXT:    [[CMP:%.*]] = icmp sgt i32 [[Y:%.*]], -1
+; CHECK-NEXT:    br i1 [[CMP]], label [[LOOP_PREHEADER:%.*]], label [[EXIT]]
+; CHECK:       loop.preheader:
+; CHECK-NEXT:    [[CMP2:%.*]] = icmp eq i32 [[Y]], 0
+; CHECK-NEXT:    br label [[LOOP:%.*]]
+; CHECK:       loop:
+; CHECK-NEXT:    br i1 [[C1]], label [[LOOP2:%.*]], label [[LOOP]]
+; CHECK:       loop.latch:
+; CHECK-NEXT:    br i1 [[CMP]], label [[LOOP]], label [[EXIT]]
+; CHECK:       loop2:
+; CHECK-NEXT:    br i1 [[CMP2]], label [[JOIN:%.*]], label [[IF:%.*]]
+; CHECK:       if:
+; CHECK-NEXT:    call void @dummy()
+; CHECK-NEXT:    br label [[JOIN]]
+; CHECK:       join:
+; CHECK-NEXT:    br i1 [[C2:%.*]], label [[LOOP2]], label [[LOOP_LATCH:%.*]]
+; CHECK:       exit:
+; CHECK-NEXT:    ret i32 0
+;
+  br i1 %c1, label %exit, label %loop.pre.preheader
+
+loop.pre.preheader:
+  %cmp = icmp sgt i32 %y, -1
+  br i1 %cmp, label %loop.preheader, label %exit
+
+loop.preheader:
+  %cmp2 = icmp eq i32 %y, 0
+  br label %loop
+
+loop:
+  br i1 %c1, label %loop2, label %loop.latch
+
+loop.latch:
+  br i1 %cmp, label %loop, label %exit
+
+loop2:
+  br i1 %cmp2, label %join, label %if
+
+if:
+  call void @dummy()
+  br label %join
+
+join:
+  br i1 %c2, label %loop2, label %loop.latch
+
+exit:
+  ret i32 0
+
+; uselistorder directives
+  uselistorder label %loop2, { 1, 0 }
+}