diff --git a/python/ql/src/Expressions/UseofInput.ql b/python/ql/src/Expressions/UseofInput.ql
index 2b11eecfa2b1..bf2a71de22e6 100644
--- a/python/ql/src/Expressions/UseofInput.ql
+++ b/python/ql/src/Expressions/UseofInput.ql
@@ -11,11 +11,12 @@
  */
 
 import python
+import semmle.python.dataflow.new.DataFlow
+import semmle.python.ApiGraphs
 
-from CallNode call, Context context, ControlFlowNode func
+from DataFlow::CallCfgNode call
 where
-  context.getAVersion().includes(2, _) and
-  call.getFunction() = func and
-  func.pointsTo(context, Value::named("input"), _) and
-  not func.pointsTo(context, Value::named("raw_input"), _)
+  major_version() = 2 and
+  call = API::builtin("input").getACall() and
+  call != API::builtin("raw_input").getACall()
 select call, "The unsafe built-in function 'input' is used in Python 2."
diff --git a/python/ql/src/semmle/python/ApiGraphs.qll b/python/ql/src/semmle/python/ApiGraphs.qll
index a530e44e85da..61c9f4c1c7f7 100644
--- a/python/ql/src/semmle/python/ApiGraphs.qll
+++ b/python/ql/src/semmle/python/ApiGraphs.qll
@@ -349,22 +349,95 @@ module API {
       )
     }
 
-    private import semmle.python.types.Builtins as Builtins
+    /** Gets the name of a known built-in. */
+    private string getBuiltInName() {
+      // These lists were created by inspecting the `builtins` and `__builtin__` modules in
+      // Python 3 and 2 respectively, using the `dir` built-in.
+      // Built-in functions and exceptions shared between Python 2 and 3
+      result in [
+          "abs", "all", "any", "bin", "bool", "bytearray", "callable", "chr", "classmethod",
+          "compile", "complex", "delattr", "dict", "dir", "divmod", "enumerate", "eval", "filter",
+          "float", "format", "frozenset", "getattr", "globals", "hasattr", "hash", "help", "hex",
+          "id", "input", "int", "isinstance", "issubclass", "iter", "len", "list", "locals", "map",
+          "max", "memoryview", "min", "next", "object", "oct", "open", "ord", "pow", "print",
+          "property", "range", "repr", "reversed", "round", "set", "setattr", "slice", "sorted",
+          "staticmethod", "str", "sum", "super", "tuple", "type", "vars", "zip", "__import__",
+          // Exceptions
+          "ArithmeticError", "AssertionError", "AttributeError", "BaseException", "BufferError",
+          "BytesWarning", "DeprecationWarning", "EOFError", "EnvironmentError", "Exception",
+          "FloatingPointError", "FutureWarning", "GeneratorExit", "IOError", "ImportError",
+          "ImportWarning", "IndentationError", "IndexError", "KeyError", "KeyboardInterrupt",
+          "LookupError", "MemoryError", "NameError", "NotImplemented", "NotImplementedError",
+          "OSError", "OverflowError", "PendingDeprecationWarning", "ReferenceError", "RuntimeError",
+          "RuntimeWarning", "StandardError", "StopIteration", "SyntaxError", "SyntaxWarning",
+          "SystemError", "SystemExit", "TabError", "TypeError", "UnboundLocalError",
+          "UnicodeDecodeError", "UnicodeEncodeError", "UnicodeError", "UnicodeTranslateError",
+          "UnicodeWarning", "UserWarning", "ValueError", "Warning", "ZeroDivisionError",
+          // Added for compatibility
+          "exec"
+        ]
+      or
+      // Built-in constants shared between Python 2 and 3
+      result in ["False", "True", "None", "NotImplemented", "Ellipsis", "__debug__"]
+      or
+      // Python 3 only
+      result in [
+          "ascii", "breakpoint", "bytes", "exec",
+          // Exceptions
+          "BlockingIOError", "BrokenPipeError", "ChildProcessError", "ConnectionAbortedError",
+          "ConnectionError", "ConnectionRefusedError", "ConnectionResetError", "FileExistsError",
+          "FileNotFoundError", "InterruptedError", "IsADirectoryError", "ModuleNotFoundError",
+          "NotADirectoryError", "PermissionError", "ProcessLookupError", "RecursionError",
+          "ResourceWarning", "StopAsyncIteration", "TimeoutError"
+        ]
+      or
+      // Python 2 only
+      result in [
+          "basestring", "cmp", "execfile", "file", "long", "raw_input", "reduce", "reload",
+          "unichr", "unicode", "xrange"
+        ]
+    }
 
     /**
      * Gets a data flow node that is likely to refer to a built-in with the name `name`.
      *
-     * Currently this is an over-approximation, and does not account for things like overwriting a
+     * Currently this is an over-approximation, and may not account for things like overwriting a
      * built-in with a different value.
      */
     private DataFlow::Node likely_builtin(string name) {
-      result.asCfgNode() =
-        any(NameNode n |
-          n.isGlobal() and
-          n.isLoad() and
-          name = n.getId() and
-          name in [any(Builtins::Builtin b).getName(), "None", "True", "False"]
-        )
+      exists(Module m |
+        result.asCfgNode() =
+          any(NameNode n |
+            possible_builtin_accessed_in_module(n, name, m) and
+            not possible_builtin_defined_in_module(name, m)
+          )
+      )
+    }
+
+    /**
+     * Holds if a global variable called `name` (which is also the name of a built-in) is assigned
+     * a value in the module `m`.
+     */
+    private predicate possible_builtin_defined_in_module(string name, Module m) {
+      exists(NameNode n |
+        not exists(LocalVariable v | n.defines(v)) and
+        n.isStore() and
+        name = n.getId() and
+        name = getBuiltInName() and
+        m = n.getEnclosingModule()
+      )
+    }
+
+    /**
+     * Holds if `n` is an access of a global variable called `name` (which is also the name of a
+     * built-in) inside the module `m`.
+     */
+    private predicate possible_builtin_accessed_in_module(NameNode n, string name, Module m) {
+      n.isGlobal() and
+      n.isLoad() and
+      name = n.getId() and
+      name = getBuiltInName() and
+      m = n.getEnclosingModule()
     }
 
     /**
diff --git a/python/ql/test/experimental/dataflow/ApiGraphs/test.py b/python/ql/test/experimental/dataflow/ApiGraphs/test.py
index 5a382f3d6cc9..f4988e41a0f9 100644
--- a/python/ql/test/experimental/dataflow/ApiGraphs/test.py
+++ b/python/ql/test/experimental/dataflow/ApiGraphs/test.py
@@ -122,14 +122,18 @@ def my_print(x):
     print = my_print
     print("these words")
 
-def local_redefine_range():
-    range = 5
-    return range
-
-def global_redefine_range():
-    global range
-    range = 6
-    return range #$ SPURIOUS: use=moduleImport("builtins").getMember("range")
+def local_redefine_chr():
+    chr = 5
+    return chr
+
+def global_redefine_chr():
+    global chr
+    chr = 6
+    return chr
+
+def what_is_chr_now():
+    # If global_redefine_chr has been run, then the following is _not_ a reference to the built-in chr
+    return chr(123) #$ MISSING: use=moduleImport("builtins").getMember("chr").getReturn()
 
 def obscured_print():
     p = print #$ use=moduleImport("builtins").getMember("print")