diff --git a/doc/install.rst b/doc/install.rst
index ba799e3..46b26f8 100644
--- a/doc/install.rst
+++ b/doc/install.rst
@@ -63,15 +63,6 @@ numpydoc_xref_aliases : dict
   aliases/shortcuts used when specifying the types of parameters.
   The keys should not have any spaces. Together with the ``intersphinx``
   extension, you can map to links in any documentation.
-  The default is an empty ``dict``.
-
-  If you have the following ``intersphinx`` namespace configuration::
-
-      intersphinx_mapping = {
-          'python': ('https://docs.python.org/3/', None),
-          'numpy': ('https://docs.scipy.org/doc/numpy', None),
-          ...
-      }
 
   The default ``numpydoc_xref_aliases`` will supply some common ``Python``
   standard library and ``NumPy`` names for you. Then for your module, a useful
diff --git a/numpydoc/docscrape.py b/numpydoc/docscrape.py
index d79992c..2b992d8 100644
--- a/numpydoc/docscrape.py
+++ b/numpydoc/docscrape.py
@@ -219,12 +219,14 @@ class NumpyDocString(Mapping):
                 yield name, self._strip(data[2:])
 
     def _parse_param_list(self, content, single_element_is_type=False):
+        content = dedent_lines(content)
         r = Reader(content)
         params = []
         while not r.eof():
             header = r.read().strip()
-            if ' : ' in header:
-                arg_name, arg_type = header.split(' : ', maxsplit=1)
+            if ' :' in header:
+                arg_name, arg_type = header.split(' :', maxsplit=1)
+                arg_name, arg_type = arg_name.strip(), arg_type.strip()
             else:
                 if single_element_is_type:
                     arg_name, arg_type = '', header
diff --git a/numpydoc/xref.py b/numpydoc/xref.py
index a4ceaf9..7c6612e 100644
--- a/numpydoc/xref.py
+++ b/numpydoc/xref.py
@@ -95,7 +95,9 @@ DEFAULT_LINKS = {
 
 
 def make_xref(param_type, xref_aliases, xref_ignore):
-    """Enclose str in a :obj: role.
+    """Parse and apply appropriate sphinx role(s) to `param_type`.
+
+    The :obj: role is the default.
 
     Parameters
     ----------
@@ -110,7 +112,7 @@ def make_xref(param_type, xref_aliases, xref_ignore):
     Returns
     -------
     out : str
-        Text with parts that may be wrapped in a
+        Text with fully-qualified names and terms that may be wrapped in a
         ``:obj:`` role.
     """
     if param_type in xref_aliases:

diff --git a/numpydoc/tests/test_docscrape.py b/numpydoc/tests/test_docscrape.py
index 2ab0218..a0b6d2e 100644
--- a/numpydoc/tests/test_docscrape.py
+++ b/numpydoc/tests/test_docscrape.py
@@ -133,7 +133,11 @@ doc_txt = '''\
      :refguide: random;distributions, random;gauss
 
   '''
-doc = NumpyDocString(doc_txt)
+
+@pytest.fixture(params=['','\n    '], ids=["flush", "newline_indented"])
+def doc(request):
+    return NumpyDocString(request.param+doc_txt)
+
 
 doc_yields_txt = """
 Test generator
@@ -169,21 +173,21 @@ c : int
 doc_sent = NumpyDocString(doc_sent_txt)
 
 
-def test_signature():
+def test_signature(doc):
     assert doc['Signature'].startswith('numpy.multivariate_normal(')
     assert doc['Signature'].endswith('spam=None)')
 
 
-def test_summary():
+def test_summary(doc):
     assert doc['Summary'][0].startswith('Draw values')
     assert doc['Summary'][-1].endswith('covariance.')
 
 
-def test_extended_summary():
+def test_extended_summary(doc):
     assert doc['Extended Summary'][0].startswith('The multivariate normal')
 
 
-def test_parameters():
+def test_parameters(doc):
     assert len(doc['Parameters']) == 4
     names = [n for n, _, _ in doc['Parameters']]
     assert all(a == b for a, b in zip(names, ['mean', 'cov', 'shape']))
@@ -205,7 +209,7 @@ def test_parameters():
     assert desc[0].startswith('The type and size')
 
 
-def test_other_parameters():
+def test_other_parameters(doc):
     assert len(doc['Other Parameters']) == 1
     assert [n for n, _, _ in doc['Other Parameters']] == ['spam']
     arg, arg_type, desc = doc['Other Parameters'][0]
@@ -213,7 +217,8 @@ def test_other_parameters():
     assert desc[0].startswith('A parrot off its mortal coil')
 
 
-def test_returns():
+
+def test_returns(doc):
     assert len(doc['Returns']) == 3
     arg, arg_type, desc = doc['Returns'][0]
     assert arg == 'out'
@@ -342,23 +347,23 @@ That should break...
                 or 'function dummy_func' in str(e))
 
 
-def test_notes():
+def test_notes(doc):
     assert doc['Notes'][0].startswith('Instead')
     assert doc['Notes'][-1].endswith('definite.')
     assert len(doc['Notes']) == 17
 
 
-def test_references():
+def test_references(doc):
     assert doc['References'][0].startswith('..')
     assert doc['References'][-1].endswith('2001.')
 
 
-def test_examples():
+def test_examples(doc):
     assert doc['Examples'][0].startswith('>>>')
     assert doc['Examples'][-1].endswith('True]')
 
 
-def test_index():
+def test_index(doc):
     assert doc['index']['default'] == 'random'
     assert len(doc['index']) == 2
     assert len(doc['index']['refguide']) == 2
@@ -382,7 +387,7 @@ def line_by_line_compare(a, b, n_lines=None):
         assert aa == bb
 
 
-def test_str():
+def test_str(doc):
     # doc_txt has the order of Notes and See Also sections flipped.
     # This should be handled automatically, and so, one thing this test does
     # is to make sure that See Also precedes Notes in the output.
@@ -921,6 +926,21 @@ doc7 = NumpyDocString("""
 def test_empty_first_line():
     assert doc7['Summary'][0].startswith('Doc starts')
 
+doc8 = NumpyDocString("""
+
+        Parameters with colon and no types:
+
+        Parameters
+        ----------
+
+        data :
+            some stuff, technically invalid
+        """)
+
+
+def test_trailing_colon():
+    assert doc8['Parameters'][0].name == 'data'
+
 
 def test_no_summary():
     str(SphinxDocString("""
diff --git a/numpydoc/tests/test_xref.py b/numpydoc/tests/test_xref.py
index 31dfacd..5d16919 100644
--- a/numpydoc/tests/test_xref.py
+++ b/numpydoc/tests/test_xref.py
@@ -1,25 +1,15 @@
 # -*- encoding:utf-8 -*-
 import pytest
-from numpydoc.xref import make_xref
-
-xref_aliases = {
-    # python
-    'sequence': ':term:`python:sequence`',
-    'iterable': ':term:`python:iterable`',
-    'string': 'str',
-    # numpy
-    'array': 'numpy.ndarray',
-    'dtype': 'numpy.dtype',
-    'ndarray': 'numpy.ndarray',
-    'matrix': 'numpy.matrix',
-    'array-like': ':term:`numpy:array_like`',
-    'array_like': ':term:`numpy:array_like`',
-}
+from numpydoc.xref import make_xref, DEFAULT_LINKS
+
+# Use the default numpydoc link mapping
+xref_aliases = DEFAULT_LINKS
+
 
 # Comes mainly from numpy
 data = r"""
 (...) array_like, float, optional
-(...) :term:`numpy:array_like`, :obj:`float`, optional
+(...) :term:`numpy:array_like`, :class:`python:float`, optional
 
 (2,) ndarray
 (2,) :obj:`ndarray <numpy.ndarray>`
@@ -31,37 +21,37 @@ data = r"""
 (..., :obj:`M`, :obj:`N`) :term:`numpy:array_like`
 
 (float, float), optional
-(:obj:`float`, :obj:`float`), optional
+(:class:`python:float`, :class:`python:float`), optional
 
 1-D array or sequence
 1-D :obj:`array <numpy.ndarray>` or :term:`python:sequence`
 
 array of str or unicode-like
-:obj:`array <numpy.ndarray>` of :obj:`str` or unicode-like
+:obj:`array <numpy.ndarray>` of :class:`python:str` or unicode-like
 
 array_like of float
-:term:`numpy:array_like` of :obj:`float`
+:term:`numpy:array_like` of :class:`python:float`
 
 bool or callable
-:obj:`bool` or :obj:`callable`
+:ref:`bool <python:bltin-boolean-values>` or :func:`python:callable`
 
 int in [0, 255]
-:obj:`int` in [0, 255]
+:class:`python:int` in [0, 255]
 
 int or None, optional
-:obj:`int` or :obj:`None`, optional
+:class:`python:int` or :data:`python:None`, optional
 
 list of str or array_like
-:obj:`list` of :obj:`str` or :term:`numpy:array_like`
+:class:`python:list` of :class:`python:str` or :term:`numpy:array_like`
 
 sequence of array_like
 :term:`python:sequence` of :term:`numpy:array_like`
 
 str or pathlib.Path
-:obj:`str` or :obj:`pathlib.Path`
+:class:`python:str` or :obj:`pathlib.Path`
 
 {'', string}, optional
-{'', :obj:`string <str>`}, optional
+{'', :class:`python:str`}, optional
 
 {'C', 'F', 'A', or 'K'}, optional
 {'C', 'F', 'A', or 'K'}, optional
@@ -70,16 +60,16 @@ str or pathlib.Path
 {'linear', 'lower', 'higher', 'midpoint', 'nearest'}
 
 {False, True, 'greedy', 'optimal'}
-{:obj:`False`, :obj:`True`, 'greedy', 'optimal'}
+{:data:`python:False`, :data:`python:True`, 'greedy', 'optimal'}
 
 {{'begin', 1}, {'end', 0}}, {string, int}
-{{'begin', 1}, {'end', 0}}, {:obj:`string <str>`, :obj:`int`}
+{{'begin', 1}, {'end', 0}}, {:class:`python:str`, :class:`python:int`}
 
 callable f'(x,*args)
-:obj:`callable` f'(x,*args)
+:func:`python:callable` f'(x,*args)
 
 callable ``fhess(x, *args)``, optional
-:obj:`callable` ``fhess(x, *args)``, optional
+:func:`python:callable` ``fhess(x, *args)``, optional
 
 spmatrix (format: ``csr``, ``bsr``, ``dia`` or coo``)
 :obj:`spmatrix` (format: ``csr``, ``bsr``, ``dia`` or coo``)
@@ -88,28 +78,28 @@ spmatrix (format: ``csr``, ``bsr``, ``dia`` or coo``)
 :ref:`strftime <strftime-strptime-behavior>`
 
 callable or :ref:`strftime <strftime-strptime-behavior>`
-:obj:`callable` or :ref:`strftime <strftime-strptime-behavior>`
+:func:`python:callable` or :ref:`strftime <strftime-strptime-behavior>`
 
 callable or :ref:`strftime behavior <strftime-strptime-behavior>`
-:obj:`callable` or :ref:`strftime behavior <strftime-strptime-behavior>`
+:func:`python:callable` or :ref:`strftime behavior <strftime-strptime-behavior>`
 
 list(int)
-:obj:`list`\(:obj:`int`)
+:class:`python:list`\(:class:`python:int`)
 
 list[int]
-:obj:`list`\[:obj:`int`]
+:class:`python:list`\[:class:`python:int`]
 
 dict(str, int)
-:obj:`dict`\(:obj:`str`, :obj:`int`)
+:class:`python:dict`\(:class:`python:str`, :class:`python:int`)
 
 dict[str,  int]
-:obj:`dict`\[:obj:`str`,  :obj:`int`]
+:class:`python:dict`\[:class:`python:str`,  :class:`python:int`]
 
 tuple(float, float)
-:obj:`tuple`\(:obj:`float`, :obj:`float`)
+:class:`python:tuple`\(:class:`python:float`, :class:`python:float`)
 
 dict[tuple(str, str), int]
-:obj:`dict`\[:obj:`tuple`\(:obj:`str`, :obj:`str`), :obj:`int`]
+:class:`python:dict`\[:class:`python:tuple`\(:class:`python:str`, :class:`python:str`), :class:`python:int`]
 """  # noqa: E501
 
 xref_ignore = {'or', 'in', 'of', 'default', 'optional'}

Wrong number of Parameter for numpy array.
```
In [1]: from numpydoc.docscrape import NumpyDocString
   ...: from numpy import array
   ...: len(NumpyDocString(array.__doc__)['Parameters'])
Out[1]: 1
```

(should be 6)

Again due to a dedent issue: 

```
$ git diff
diff --git a/numpydoc/docscrape.py b/numpydoc/docscrape.py
index d79992c..3db20fe 100644
--- a/numpydoc/docscrape.py
+++ b/numpydoc/docscrape.py
@@ -219,6 +219,7 @@ class NumpyDocString(Mapping):
                 yield name, self._strip(data[2:])

     def _parse_param_list(self, content, single_element_is_type=False):
+        content = dedent_lines(content)
         r = Reader(content)
         params = []
         while not r.eof():
```

Fixes it. 

Not quite sure why it is not found in tests...



numpydoc/tests/test_docscrape.py::test_trailing_colon
numpydoc/tests/test_docscrape.py::test_signature[flush] numpydoc/tests/test_docscrape.py::test_signature[newline_indented] numpydoc/tests/test_docscrape.py::test_summary[flush] numpydoc/tests/test_docscrape.py::test_summary[newline_indented] numpydoc/tests/test_docscrape.py::test_extended_summary[flush] numpydoc/tests/test_docscrape.py::test_extended_summary[newline_indented] numpydoc/tests/test_docscrape.py::test_parameters[flush] numpydoc/tests/test_docscrape.py::test_parameters[newline_indented] numpydoc/tests/test_docscrape.py::test_other_parameters[flush] numpydoc/tests/test_docscrape.py::test_other_parameters[newline_indented] numpydoc/tests/test_docscrape.py::test_returns[flush] numpydoc/tests/test_docscrape.py::test_returns[newline_indented] numpydoc/tests/test_docscrape.py::test_yields numpydoc/tests/test_docscrape.py::test_sent numpydoc/tests/test_docscrape.py::test_returnyield numpydoc/tests/test_docscrape.py::test_section_twice numpydoc/tests/test_docscrape.py::test_notes[flush] numpydoc/tests/test_docscrape.py::test_notes[newline_indented] numpydoc/tests/test_docscrape.py::test_references[flush] numpydoc/tests/test_docscrape.py::test_references[newline_indented] numpydoc/tests/test_docscrape.py::test_examples[flush] numpydoc/tests/test_docscrape.py::test_examples[newline_indented] numpydoc/tests/test_docscrape.py::test_index[flush] numpydoc/tests/test_docscrape.py::test_index[newline_indented] numpydoc/tests/test_docscrape.py::test_str[flush] numpydoc/tests/test_docscrape.py::test_str[newline_indented] numpydoc/tests/test_docscrape.py::test_yield_str numpydoc/tests/test_docscrape.py::test_receives_str numpydoc/tests/test_docscrape.py::test_no_index_in_str numpydoc/tests/test_docscrape.py::test_sphinx_str numpydoc/tests/test_docscrape.py::test_sphinx_yields_str numpydoc/tests/test_docscrape.py::test_parameters_without_extended_description numpydoc/tests/test_docscrape.py::test_escape_stars numpydoc/tests/test_docscrape.py::test_empty_extended_summary numpydoc/tests/test_docscrape.py::test_raises numpydoc/tests/test_docscrape.py::test_warns numpydoc/tests/test_docscrape.py::test_see_also[] numpydoc/tests/test_docscrape.py::test_see_also[\n numpydoc/tests/test_docscrape.py::test_see_also_parse_error numpydoc/tests/test_docscrape.py::test_see_also_print numpydoc/tests/test_docscrape.py::test_see_also_trailing_comma_warning numpydoc/tests/test_docscrape.py::test_unknown_section numpydoc/tests/test_docscrape.py::test_empty_first_line numpydoc/tests/test_docscrape.py::test_no_summary numpydoc/tests/test_docscrape.py::test_unicode numpydoc/tests/test_docscrape.py::test_plot_examples numpydoc/tests/test_docscrape.py::test_use_blockquotes numpydoc/tests/test_docscrape.py::test_class_members numpydoc/tests/test_docscrape.py::test_duplicate_signature numpydoc/tests/test_docscrape.py::test_class_members_doc numpydoc/tests/test_docscrape.py::test_class_members_doc_sphinx numpydoc/tests/test_docscrape.py::test_class_attributes_as_member_list numpydoc/tests/test_docscrape.py::test_templated_sections numpydoc/tests/test_docscrape.py::test_nonstandard_property numpydoc/tests/test_docscrape.py::test_args_and_kwargs numpydoc/tests/test_docscrape.py::test_autoclass numpydoc/tests/test_docscrape.py::test_xref numpydoc/tests/test_xref.py::test_make_xref[(...) numpydoc/tests/test_xref.py::test_make_xref[(2,) numpydoc/tests/test_xref.py::test_make_xref[(...,M,N) numpydoc/tests/test_xref.py::test_make_xref[(..., numpydoc/tests/test_xref.py::test_make_xref[(float, numpydoc/tests/test_xref.py::test_make_xref[1-D numpydoc/tests/test_xref.py::test_make_xref[array numpydoc/tests/test_xref.py::test_make_xref[array_like numpydoc/tests/test_xref.py::test_make_xref[bool numpydoc/tests/test_xref.py::test_make_xref[int numpydoc/tests/test_xref.py::test_make_xref[list numpydoc/tests/test_xref.py::test_make_xref[sequence numpydoc/tests/test_xref.py::test_make_xref[str numpydoc/tests/test_xref.py::test_make_xref[{'', numpydoc/tests/test_xref.py::test_make_xref[{'C', numpydoc/tests/test_xref.py::test_make_xref[{'linear', numpydoc/tests/test_xref.py::test_make_xref[{False, numpydoc/tests/test_xref.py::test_make_xref[{{'begin', numpydoc/tests/test_xref.py::test_make_xref[callable numpydoc/tests/test_xref.py::test_make_xref[spmatrix numpydoc/tests/test_xref.py::test_make_xref[:ref:`strftime numpydoc/tests/test_xref.py::test_make_xref[list(int)-:class:`python:list`\\(:class:`python:int`)] numpydoc/tests/test_xref.py::test_make_xref[list[int]-:class:`python:list`\\[:class:`python:int`]] numpydoc/tests/test_xref.py::test_make_xref[dict(str, numpydoc/tests/test_xref.py::test_make_xref[dict[str, numpydoc/tests/test_xref.py::test_make_xref[tuple(float, numpydoc/tests/test_xref.py::test_make_xref[dict[tuple(str,