diff --git a/clang-tools-extra/clang-tidy/misc/RedundantExpressionCheck.cpp b/clang-tools-extra/clang-tidy/misc/RedundantExpressionCheck.cpp
--- a/clang-tools-extra/clang-tidy/misc/RedundantExpressionCheck.cpp
+++ b/clang-tools-extra/clang-tidy/misc/RedundantExpressionCheck.cpp
@@ -569,6 +569,7 @@
   std::string SwapId = (Id + "-swap").str();
   std::string NegateId = (Id + "-negate").str();
   std::string OverloadId = (Id + "-overload").str();
+  std::string ConstId = (Id + "-const").str();
 
   const auto RelationalExpr = ignoringParenImpCasts(binaryOperator(
       isComparisonOperator(), expr().bind(Id),
@@ -600,7 +601,8 @@
       cxxOperatorCallExpr(
           hasAnyOverloadedOperatorName("==", "!=", "<", "<=", ">", ">="),
           // Filter noisy false positives.
-          unless(isMacro()), unless(isInTemplateInstantiation()))
+          unless(isMacro()), unless(isInTemplateInstantiation()),
+          hasRHS(ignoringParenImpCasts(integerLiteral().bind(ConstId))))
           .bind(OverloadId);
 
   return anyOf(RelationalExpr, CastExpr, NegateRelationalExpr,
@@ -683,6 +685,9 @@
     OperandExpr = OverloadedOperatorExpr;
     Opcode = BinaryOperator::getOverloadedOpcode(OverloadedOperatorExpr->getOperator());
 
+    if (!retrieveIntegerConstantExpr(Result, Id, Value, ConstExpr))
+      return false;
+
     return BinaryOperator::isComparisonOp(Opcode);
   } else {
     return false;
diff --git a/clang-tools-extra/test/clang-tidy/checkers/misc-redundant-expression.cpp b/clang-tools-extra/test/clang-tidy/checkers/misc-redundant-expression.cpp
--- a/clang-tools-extra/test/clang-tidy/checkers/misc-redundant-expression.cpp
+++ b/clang-tools-extra/test/clang-tidy/checkers/misc-redundant-expression.cpp
@@ -453,6 +453,11 @@
   if (s1 >= 1 || s1 <= 1) return true;
   // CHECK-MESSAGES: :[[@LINE-1]]:15: warning: logical expression is always true
 
+  // Test for absence of false positives (issue #54011).
+  if (s1 == 1 || s1 == 2) return true;
+  if (s1 > 1 && s1 < 3) return true;
+  if (s1 >= 2 || s1 <= 0) return true;
+
   // Test for overloaded operators that may modify their params.
   S2 s2;
   if (s2 == 1 || s2 != 1) return true;