Index: clang-tidy/readability/ContainerSizeEmptyCheck.cpp
===================================================================
--- clang-tidy/readability/ContainerSizeEmptyCheck.cpp
+++ clang-tidy/readability/ContainerSizeEmptyCheck.cpp
@@ -29,11 +29,11 @@
   if (!getLangOpts().CPlusPlus)
     return;
 
-  const auto stlContainer = hasAnyName(
-      "array", "basic_string", "deque", "forward_list", "list", "map",
-      "multimap", "multiset", "priority_queue", "queue", "set", "stack",
-      "unordered_map", "unordered_multimap", "unordered_multiset",
-      "unordered_set", "vector");
+  const auto validContainer = namedDecl(
+      has(functionDecl(
+          isPublic(), hasName("size"), returns(isInteger()),
+          unless(anyOf(returns(isAnyCharacter()), returns(booleanType()))))),
+      has(functionDecl(isPublic(), hasName("empty"), returns(booleanType()))));
 
   const auto WrongUse = anyOf(
       hasParent(binaryOperator(
@@ -50,9 +50,9 @@
 
   Finder->addMatcher(
       cxxMemberCallExpr(
-          on(expr(anyOf(hasType(namedDecl(stlContainer)),
-                        hasType(pointsTo(namedDecl(stlContainer))),
-                        hasType(references(namedDecl(stlContainer)))))
+          on(expr(anyOf(hasType(namedDecl(validContainer)),
+                        hasType(pointsTo(namedDecl(validContainer))),
+                        hasType(references(namedDecl(validContainer)))))
                  .bind("STLObject")),
           callee(cxxMethodDecl(hasName("size"))), WrongUse)
           .bind("SizeCallExpr"),
Index: test/clang-tidy/readability-container-size-empty.cpp
===================================================================
--- test/clang-tidy/readability-container-size-empty.cpp
+++ test/clang-tidy/readability-container-size-empty.cpp
@@ -24,9 +24,34 @@
 };
 }
 
-
 }
 
+template <typename T>
+class TemplatedContainer {
+public:
+  int size();
+  bool empty();
+};
+
+template <typename T>
+class PrivateEmpty {
+public:
+  int size();
+private:
+  bool empty();
+};
+
+struct BoolSize {
+  bool size();
+  bool empty();
+};
+
+struct EnumSize {
+  enum E { one };
+  enum E size() const;
+  bool empty();
+};
+
 int main() {
   std::set<int> intSet;
   std::string str;
@@ -127,6 +152,110 @@
     ;
   // CHECK-MESSAGES: :[[@LINE-2]]:7: warning: the 'empty' method should be used
   // CHECK-FIXES: {{^  }}if (vect4.empty()){{$}}
+
+  TemplatedContainer<void> templated_container;
+  if (templated_container.size() == 0)
+    ;
+  // CHECK-MESSAGES: :[[@LINE-2]]:7: warning: the 'empty' method should be used
+  // CHECK-FIXES: {{^  }}if (templated_container.empty()){{$}}
+  if (templated_container.size() != 0)
+    ;
+  // CHECK-MESSAGES: :[[@LINE-2]]:7: warning: the 'empty' method should be used
+  // CHECK-FIXES: {{^  }}if (!templated_container.empty()){{$}}
+  if (0 == templated_container.size())
+    ;
+  // CHECK-MESSAGES: :[[@LINE-2]]:12: warning: the 'empty' method should be used
+  // CHECK-FIXES: {{^  }}if (templated_container.empty()){{$}}
+  if (0 != templated_container.size())
+    ;
+  // CHECK-MESSAGES: :[[@LINE-2]]:12: warning: the 'empty' method should be used
+  // CHECK-FIXES: {{^  }}if (!templated_container.empty()){{$}}
+  if (templated_container.size() > 0)
+    ;
+  // CHECK-MESSAGES: :[[@LINE-2]]:7: warning: the 'empty' method should be used
+  // CHECK-FIXES: {{^  }}if (!templated_container.empty()){{$}}
+  if (0 < templated_container.size())
+    ;
+  // CHECK-MESSAGES: :[[@LINE-2]]:11: warning: the 'empty' method should be used
+  // CHECK-FIXES: {{^  }}if (!templated_container.empty()){{$}}
+  if (templated_container.size() < 1)
+    ;
+  // CHECK-MESSAGES: :[[@LINE-2]]:7: warning: the 'empty' method should be used
+  // CHECK-FIXES: {{^  }}if (templated_container.empty()){{$}}
+  if (1 > templated_container.size())
+    ;
+  // CHECK-MESSAGES: :[[@LINE-2]]:11: warning: the 'empty' method should be used
+  // CHECK-FIXES: {{^  }}if (templated_container.empty()){{$}}
+  if (templated_container.size() >= 1)
+    ;
+  // CHECK-MESSAGES: :[[@LINE-2]]:7: warning: the 'empty' method should be used
+  // CHECK-FIXES: {{^  }}if (!templated_container.empty()){{$}}
+  if (1 <= templated_container.size())
+    ;
+  // CHECK-MESSAGES: :[[@LINE-2]]:12: warning: the 'empty' method should be used
+  // CHECK-FIXES: {{^  }}if (!templated_container.empty()){{$}}
+  if (templated_container.size() > 1) // no warning
+    ;
+  if (1 < templated_container.size()) // no warning
+    ;
+  if (templated_container.size() <= 1) // no warning
+    ;
+  if (1 >= templated_container.size()) // no warning
+    ;
+  if (!templated_container.size())
+    ;
+  // CHECK-MESSAGES: :[[@LINE-2]]:8: warning: the 'empty' method should be used
+  // CHECK-FIXES: {{^  }}if (templated_container.empty()){{$}}
+  if (templated_container.size())
+    ;
+  // CHECK-MESSAGES: :[[@LINE-2]]:7: warning: the 'empty' method should be used
+  // CHECK-FIXES: {{^  }}if (!templated_container.empty()){{$}}
+
+  if (templated_container.empty())
+    ;
+
+  // No warnings expected.
+  PrivateEmpty<void> private_empty;
+  if (private_empty.size() == 0)
+    ;
+  if (private_empty.size() != 0)
+    ;
+  if (0 == private_empty.size())
+    ;
+  if (0 != private_empty.size())
+    ;
+  if (private_empty.size() > 0)
+    ;
+  if (0 < private_empty.size())
+    ;
+  if (private_empty.size() < 1)
+    ;
+  if (1 > private_empty.size())
+    ;
+  if (private_empty.size() >= 1)
+    ;
+  if (1 <= private_empty.size())
+    ;
+  if (private_empty.size() > 1)
+    ;
+  if (1 < private_empty.size())
+    ;
+  if (private_empty.size() <= 1)
+    ;
+  if (1 >= private_empty.size())
+    ;
+  if (!private_empty.size())
+    ;
+  if (private_empty.size())
+    ;
+
+  // Types with weird size() return type.
+  BoolSize bs;
+  if (bs.size() == 0)
+    ;
+  EnumSize es;
+  if (es.size() == 0)
+    ;
 }
 
 #define CHECKSIZE(x) if (x.size())
@@ -142,6 +271,16 @@
   CHECKSIZE(v);
   // CHECK-MESSAGES: :[[@LINE-1]]:13: warning: the 'empty' method should be used
   // CHECK-MESSAGES: CHECKSIZE(v);
+
+  TemplatedContainer<T> templated_container;
+  if (templated_container.size())
+    ;
+  // CHECK-MESSAGES: :[[@LINE-2]]:7: warning: the 'empty' method should be used
+  // CHECK-FIXES: {{^  }}if (!templated_container.empty()){{$}}
+  // CHECK-FIXES-NEXT: ;
+  CHECKSIZE(templated_container);
+  // CHECK-MESSAGES: :[[@LINE-1]]:13: warning: the 'empty' method should be used
+  // CHECK-MESSAGES: CHECKSIZE(templated_container);
 }
 
 void g() {