Index: clang-tools-extra/clang-tidy/utils/ExceptionAnalyzer.cpp
===================================================================
--- clang-tools-extra/clang-tidy/utils/ExceptionAnalyzer.cpp
+++ clang-tools-extra/clang-tidy/utils/ExceptionAnalyzer.cpp
@@ -192,8 +192,27 @@
     Results.merge(Uncaught);
   } else if (const auto *Call = dyn_cast<CallExpr>(St)) {
     if (const FunctionDecl *Func = Call->getDirectCallee()) {
-      ExceptionInfo Excs = throwsException(Func, CallStack);
-      Results.merge(Excs);
+      bool MightThrow;
+
+      switch (Func->getExceptionSpecType()) {
+      case EST_DynamicNone:
+      case EST_NoThrow:
+      case EST_BasicNoexcept:
+      case EST_DependentNoexcept: // Let's be optimistic here (necessary e.g.
+                                  // for variant assignment; see PR#52254)
+      case EST_NoexceptTrue:
+        MightThrow = false;
+        break;
+
+      default:
+        MightThrow = true;
+        break;
+      }
+
+      if (MightThrow) {
+        ExceptionInfo Excs = throwsException(Func, CallStack);
+        Results.merge(Excs);
+      }
     }
   } else {
     for (const Stmt *Child : St->children()) {
Index: clang-tools-extra/test/clang-tidy/checkers/bugprone-exception-escape.cpp
===================================================================
--- clang-tools-extra/test/clang-tidy/checkers/bugprone-exception-escape.cpp
+++ clang-tools-extra/test/clang-tidy/checkers/bugprone-exception-escape.cpp
@@ -288,6 +288,29 @@
   return recursion_helper(n);
 }
 
+// The following functions all incorrectly throw exceptions, *but* calling them
+// should not yield a warning because they are marked as noexcept (or similar).
+void est_dynamic_none() throw() { throw 42; }
+// CHECK-MESSAGES: :[[@LINE-1]]:6: warning: an exception may be thrown in function 'est_dynamic_none' which should not throw exceptions
+void est_basic_noexcept() noexcept { throw 42; }
+// CHECK-MESSAGES: :[[@LINE-1]]:6: warning: an exception may be thrown in function 'est_basic_noexcept' which should not throw exceptions
+void est_noexcept_true() noexcept(true) { throw 42; }
+// CHECK-MESSAGES: :[[@LINE-1]]:6: warning: an exception may be thrown in function 'est_noexcept_true' which should not throw exceptions
+template <typename T>
+void est_dependent_noexcept() noexcept(T::should_throw) { throw 42; }
+// CHECK-MESSAGES: :[[@LINE-1]]:6: warning: an exception may be thrown in function 'est_dependent_noexcept<ShouldThrow<true>>' which should not throw exceptions
+template <bool B>
+struct ShouldThrow {
+  static const bool should_throw = B;
+};
+
+void only_calls_non_throwing() noexcept {
+  est_dynamic_none();
+  est_basic_noexcept();
+  est_noexcept_true();
+  est_dependent_noexcept<ShouldThrow<true>>();
+}
+
 int main() {
   // CHECK-MESSAGES: :[[@LINE-1]]:5: warning: an exception may be thrown in function 'main' which should not throw exceptions
   throw 1;