diff --git a/Lib/test/test_format.py b/Lib/test/test_format.py
index a9b3170..8bf5d6e 100644
--- a/Lib/test/test_format.py
+++ b/Lib/test/test_format.py
@@ -219,8 +219,8 @@
     test_exc(unicode('abc %\u3000','raw-unicode-escape'), 1, ValueError,
              "unsupported format character '?' (0x3000) at index 5")
 
-test_exc('%d', '1', TypeError, "int argument required")
-test_exc('%g', '1', TypeError, "float argument required")
+test_exc('%d', '1', TypeError, "int argument required, not str")
+test_exc('%g', '1', TypeError, "float argument required, not str")
 test_exc('no format', '1', TypeError,
          "not all arguments converted during string formatting")
 test_exc('no format', u'1', TypeError,
diff --git a/Misc/NEWS b/Misc/NEWS
index 4f1df73..6fd73f6 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -12,6 +12,9 @@
 Core and builtins
 -----------------
 
+- Patch #1586791: Better exception messages for some operations on strings,
+  tuples and lists.
+
 - Bug #1067760: Deprecate passing floats to file.seek.
 
 - Bug #1591996: Correctly forward exception in instance_contains().
diff --git a/Objects/listobject.c b/Objects/listobject.c
index a1ac2cb..3083b5f 100644
--- a/Objects/listobject.c
+++ b/Objects/listobject.c
@@ -946,9 +946,10 @@
 	if (res == NULL)
 		return -1;
 	if (!PyInt_Check(res)) {
+		PyErr_Format(PyExc_TypeError,
+			     "comparison function must return int, not %.200s",
+			     res->ob_type->tp_name);
 		Py_DECREF(res);
-		PyErr_SetString(PyExc_TypeError,
-				"comparison function must return int");
 		return -1;
 	}
 	i = PyInt_AsLong(res);
@@ -2491,8 +2492,9 @@
 		}
 	}
 	else {
-		PyErr_SetString(PyExc_TypeError,
-				"list indices must be integers");
+		PyErr_Format(PyExc_TypeError,
+			     "list indices must be integers, not %.200s",
+			     item->ob_type->tp_name);
 		return NULL;
 	}
 }
@@ -2635,8 +2637,9 @@
 		}
 	}
 	else {
-		PyErr_SetString(PyExc_TypeError,
-				"list indices must be integers");
+		PyErr_Format(PyExc_TypeError,
+			     "list indices must be integers, not %.200s",
+			     item->ob_type->tp_name);
 		return -1;
 	}
 }
diff --git a/Objects/stringobject.c b/Objects/stringobject.c
index aa2fd87..5d31c38 100644
--- a/Objects/stringobject.c
+++ b/Objects/stringobject.c
@@ -1071,8 +1071,9 @@
 			return PyUnicode_Contains(str_obj, sub_obj);
 #endif
 		if (!PyString_Check(sub_obj)) {
-			PyErr_SetString(PyExc_TypeError,
-			    "'in <string>' requires string as left operand");
+			PyErr_Format(PyExc_TypeError,
+			    "'in <string>' requires string as left operand, "
+			    "not %.200s", sub_obj->ob_type->tp_name);
 			return -1;
 		}
 	}
@@ -1240,8 +1241,9 @@
 		}
 	}
 	else {
-		PyErr_SetString(PyExc_TypeError,
-				"string indices must be integers");
+		PyErr_Format(PyExc_TypeError,
+			     "string indices must be integers, not %.200s",
+			     item->ob_type->tp_name);
 		return NULL;
 	}
 }
@@ -4148,7 +4150,8 @@
 	double x;
 	x = PyFloat_AsDouble(v);
 	if (x == -1.0 && PyErr_Occurred()) {
-		PyErr_SetString(PyExc_TypeError, "float argument required");
+		PyErr_Format(PyExc_TypeError, "float argument required, "
+			     "not %.200s", v->ob_type->tp_name);
 		return -1;
 	}
 	if (prec < 0)
@@ -4343,7 +4346,8 @@
 
 	x = PyInt_AsLong(v);
 	if (x == -1 && PyErr_Occurred()) {
-		PyErr_SetString(PyExc_TypeError, "int argument required");
+		PyErr_Format(PyExc_TypeError, "int argument required, not %.200s",
+			     v->ob_type->tp_name);
 		return -1;
 	}
 	if (x < 0 && type == 'u') {
diff --git a/Objects/tupleobject.c b/Objects/tupleobject.c
index 6f3711f..c85b35a 100644
--- a/Objects/tupleobject.c
+++ b/Objects/tupleobject.c
@@ -620,8 +620,9 @@
 		}
 	}
 	else {
-		PyErr_SetString(PyExc_TypeError, 
-				"tuple indices must be integers");
+		PyErr_Format(PyExc_TypeError, 
+			     "tuple indices must be integers, not %.200s",
+			     item->ob_type->tp_name);
 		return NULL;
 	}
 }