diff --git a/numpy/add_newdocs.py b/numpy/add_newdocs.py
index baf5285f0859..d7a8569fa174 100644
--- a/numpy/add_newdocs.py
+++ b/numpy/add_newdocs.py
@@ -3796,12 +3796,15 @@
 
 add_newdoc('numpy.lib._compiled_base', 'bincount',
     """
-    bincount(x, weights=None)
+    bincount(x, weights=None, minlength=None)
 
     Count number of occurrences of each value in array of non-negative ints.
 
     The number of bins (of size 1) is one larger than the largest value in
-    `x`. Each bin gives the number of occurrences of its index value in `x`.
+    `x`. If `minlength` is specified, there will be at least this number
+    of bins in the output array (though it will be longer if necessary,
+    depending on the contents of `x`).
+    Each bin gives the number of occurrences of its index value in `x`.
     If `weights` is specified the input array is weighted by it, i.e. if a
     value ``n`` is found at position ``i``, ``out[n] += weight[i]`` instead
     of ``out[n] += 1``.
@@ -3812,6 +3815,8 @@
         Input array.
     weights : array_like, optional
         Weights, array of the same shape as `x`.
+    minlength : integer, optional
+        A minimum number of bins for the output array.
 
     Returns
     -------
@@ -3823,7 +3828,7 @@
     ------
     ValueError
         If the input is not 1-dimensional, or contains elements with negative
-        values.
+        values, or if `minlength` is non-positive.
     TypeError
         If the type of the input is float or complex.
 
diff --git a/numpy/lib/src/_compiled_base.c b/numpy/lib/src/_compiled_base.c
index 466fa0202ce1..627fc32868d1 100644
--- a/numpy/lib/src/_compiled_base.c
+++ b/numpy/lib/src/_compiled_base.c
@@ -90,27 +90,29 @@ mnx (intp *i , intp len)
 /*
  * arr_bincount is registered as bincount.
  *
- * bincount accepts one or two arguments. The first is an array of
- * non-negative integers and the second, if present, is an array of weights,
- * which must be promotable to double.  Call these arguments list and
+ * bincount accepts one, two or three arguments. The first is an array of
+ * non-negative integers The second, if present, is an array of weights,
+ * which must be promotable to double. Call these arguments list and
  * weight. Both must be one-dimensional with len(weight) == len(list). If
  * weight is not present then bincount(list)[i] is the number of occurrences
  * of i in list.  If weight is present then bincount(self,list, weight)[i]
  * is the sum of all weight[j] where list [j] == i.  Self is not used.
+ * The third argument, if present, is a minimum length desired for the
+ * output array.
  */
 static PyObject *
 arr_bincount(PyObject *NPY_UNUSED(self), PyObject *args, PyObject *kwds)
 {
     PyArray_Descr *type;
-    PyObject *list = NULL, *weight=Py_None;
+    PyObject *list = NULL, *weight=Py_None, *mlength=Py_None;
     PyObject *lst=NULL, *ans=NULL, *wts=NULL;
-    intp *numbers, *ians, len , mxi, mni, ans_size;
+    intp *numbers, *ians, len , mxi, mni, ans_size, minlength;
     int i;
     double *weights , *dans;
-    static char *kwlist[] = {"list", "weights", NULL};
+    static char *kwlist[] = {"list", "weights", "minlength", NULL};
 
-    if (!PyArg_ParseTupleAndKeywords(args, kwds, "O|O",
-                kwlist, &list, &weight)) {
+    if (!PyArg_ParseTupleAndKeywords(args, kwds, "O|OO",
+                kwlist, &list, &weight, &mlength)) {
             goto fail;
     }
     if (!(lst = PyArray_ContiguousFromAny(list, PyArray_INTP, 1, 1))) {
@@ -131,6 +133,20 @@ arr_bincount(PyObject *NPY_UNUSED(self), PyObject *args, PyObject *kwds)
         goto fail;
     }
     ans_size = numbers [mxi] + 1;
+    if (mlength != Py_None) {
+        if (!(minlength = PyArray_PyIntAsIntp(mlength))) {
+            goto fail;
+        }
+        if (minlength <= 0) {
+            /* superfluous, but may catch incorrect usage */
+            PyErr_SetString(PyExc_ValueError,
+                    "minlength must be positive");
+            goto fail;
+        }
+        if (ans_size < minlength) {
+            ans_size = minlength;
+        }
+    }
     type = PyArray_DescrFromType(PyArray_INTP);
     if (weight == Py_None) {
         if (!(ans = PyArray_Zeros(1, &ans_size, type, 0))) {
diff --git a/numpy/lib/tests/test_function_base.py b/numpy/lib/tests/test_function_base.py
index 4df13e5f93d3..700798e76f7b 100644
--- a/numpy/lib/tests/test_function_base.py
+++ b/numpy/lib/tests/test_function_base.py
@@ -1026,6 +1026,21 @@ def test_simple_weight2(self):
         y = np.bincount(x, w)
         assert_array_equal(y, np.array([0, 0.2, 0.5, 0, 0.5, 0.1]))
 
+    def test_with_minlength(self):
+        x = np.array([0, 1, 0, 1, 1])
+        y = np.bincount(x, minlength=3)
+        assert_array_equal(y, np.array([2, 3, 0]))
+
+    def test_with_minlength_smaller_than_maxvalue(self):
+        x = np.array([0, 1, 1, 2, 2, 3, 3])
+        y = np.bincount(x, minlength=2)
+        assert_array_equal(y, np.array([1, 2, 2, 2]))
+
+    def test_with_minlength_and_weights(self):
+        x = np.array([1, 2, 4, 5, 2])
+        w = np.array([0.2, 0.3, 0.5, 0.1, 0.2])
+        y = np.bincount(x, w, 8)
+        assert_array_equal(y, np.array([0, 0.2, 0.5, 0, 0.5, 0.1, 0, 0]))
 
 class TestInterp(TestCase):
     def test_exceptions(self):