diff --git a/lib/checkclass.cpp b/lib/checkclass.cpp
index 9694827ec..7f662b5aa 100644
--- a/lib/checkclass.cpp
+++ b/lib/checkclass.cpp
@@ -1734,7 +1734,7 @@ void CheckClass::checkConst()
                     continue;
             } else if (func->isOperator() && Token::Match(previous, ";|{|}|public:|private:|protected:")) { // Operator without return type: conversion operator
                 const std::string& opName = func->tokenDef->str();
-                if (opName.compare(8, 5, "const") != 0 && opName.back() == '&')
+                if (opName.compare(8, 5, "const") != 0 && (opName.back() == '&' || opName.back() == '*'))
                     continue;
             } else {
                 // don't warn for unknown types..
diff --git a/test/testclass.cpp b/test/testclass.cpp
index 3e1539cae..95b95242f 100644
--- a/test/testclass.cpp
+++ b/test/testclass.cpp
@@ -3320,12 +3320,28 @@ private:
     }
 
     void constoperator4() {
+        // #7953
+        checkConst("class A {\n"
+                   "    int c;\n"
+                   "public:\n"
+                   "    operator int*() { return &c; };\n"
+                   "};");
+        ASSERT_EQUALS("", errout.str());
+
+        checkConst("class A {\n"
+                   "    int c;\n"
+                   "public:\n"
+                   "    operator const int*() { return &c; };\n"
+                   "};");
+        ASSERT_EQUALS("[test.cpp:4]: (style, inconclusive) Technically the member function 'A::operatorconstint*' can be const.\n", errout.str());
+
+        // #2375
         checkConst("struct Fred {\n"
                    "    int array[10];\n"
                    "    typedef int* (Fred::*UnspecifiedBoolType);\n"
                    "    operator UnspecifiedBoolType() { };\n"
                    "};");
-        ASSERT_EQUALS("[test.cpp:4]: (style, inconclusive) Technically the member function 'Fred::operatorint**' can be const.\n", errout.str());
+        TODO_ASSERT_EQUALS("[test.cpp:4]: (style, inconclusive) Technically the member function 'Fred::operatorint**' can be const.\n", "", errout.str());
 
         checkConst("struct Fred {\n"
                    "    int array[10];\n"