diff --git a/package/CHANGELOG b/package/CHANGELOG
index 5410e0f6153..8c5f6f69d8d 100644
--- a/package/CHANGELOG
+++ b/package/CHANGELOG
@@ -86,6 +86,9 @@ Enhancements
     explicit in the topology (Issue #2468, PR #2775)
 
 Changes
+  * removes deprecated `as_Universe` function from MDAnalysis.core.universe,
+    as a result :class:`MDAnalysis.analysis.leaflet.LeafletFinder` now only
+    accepts Universes for its `universe` argument (Issue #2920)
   * deprecated NumPy type aliases have been replaced with their actual types
     (see upstream NumPy PR 14882), and our pytest configuration will raise an
     error for any violation when testing with development NumPy builds
diff --git a/package/MDAnalysis/__init__.py b/package/MDAnalysis/__init__.py
index 49307f2df84..3e67264d30c 100644
--- a/package/MDAnalysis/__init__.py
+++ b/package/MDAnalysis/__init__.py
@@ -150,7 +150,7 @@
 
 """
 
-__all__ = ['Universe', 'as_Universe', 'Writer', 'fetch_mmtf',
+__all__ = ['Universe', 'Writer', 'fetch_mmtf',
            'AtomGroup', 'ResidueGroup', 'SegmentGroup']
 
 import logging
@@ -202,7 +202,7 @@
 from . import units
 
 # Bring some often used objects into the current namespace
-from .core.universe import Universe, as_Universe, Merge
+from .core.universe import Universe, Merge
 from .core.groups import AtomGroup, ResidueGroup, SegmentGroup
 from .coordinates.core import writer as Writer
 
diff --git a/package/MDAnalysis/analysis/leaflet.py b/package/MDAnalysis/analysis/leaflet.py
index b9416a381c7..1749faf593d 100644
--- a/package/MDAnalysis/analysis/leaflet.py
+++ b/package/MDAnalysis/analysis/leaflet.py
@@ -93,9 +93,8 @@ class LeafletFinder(object):
 
     Parameters
     ----------
-    universe : Universe or str
-        :class:`MDAnalysis.Universe` or a file name (e.g., in PDB or
-        GRO format)
+    universe : Universe
+        :class:`~MDAnalysis.core.universe.Universe` object.
     select : AtomGroup or str
         A AtomGroup instance or a
         :meth:`Universe.select_atoms` selection string
@@ -119,7 +118,8 @@ class LeafletFinder(object):
     consecutively, starting at 0. To obtain the atoms in the input structure
     use :meth:`LeafletFinder.groups`::
 
-       L = LeafletFinder(PDB, 'name P*')
+       u_PDB = mda.Universe(PDB)
+       L = LeafletFinder(u_PDB, 'name P*')
        leaflet0 = L.groups(0)
        leaflet1 = L.groups(1)
 
@@ -132,12 +132,15 @@ class LeafletFinder(object):
 
        leaflet0.residues.atoms
 
+
     .. versionchanged:: 1.0.0
        Changed `selection` keyword to `select`
+    .. versionchanged:: 2.0.0
+       The universe keyword no longer accepts non-Universe arguments. Please
+       create a :class:`~MDAnalysis.core.universe.Universe` first.
     """
 
     def __init__(self, universe, select, cutoff=15.0, pbc=False, sparse=None):
-        universe = core.universe.as_Universe(universe)
         self.universe = universe
         self.selectionstring = select
         if isinstance(self.selectionstring, core.groups.AtomGroup):
diff --git a/package/MDAnalysis/core/universe.py b/package/MDAnalysis/core/universe.py
index cbf8041359a..9c3ac4c859b 100644
--- a/package/MDAnalysis/core/universe.py
+++ b/package/MDAnalysis/core/universe.py
@@ -1324,32 +1324,6 @@ def from_smiles(cls, smiles, sanitize=True, addHs=True,
         return cls(mol, **kwargs)
 
 
-# TODO: what is the point of this function???
-def as_Universe(*args, **kwargs):
-    """Return a universe from the input arguments.
-
-    1. If the first argument is a universe, just return it::
-
-         as_Universe(universe) --> universe
-
-    2. Otherwise try to build a universe from the first or the first
-       and second argument::
-
-         as_Universe(PDB, **kwargs) --> Universe(PDB, **kwargs)
-         as_Universe(PSF, DCD, **kwargs) --> Universe(PSF, DCD, **kwargs)
-         as_Universe(*args, **kwargs) --> Universe(*args, **kwargs)
-
-    Returns
-    -------
-    :class:`~MDAnalysis.core.groups.Universe`
-    """
-    if len(args) == 0:
-        raise TypeError("as_Universe() takes at least one argument (%d given)" % len(args))
-    elif len(args) == 1 and isinstance(args[0], Universe):
-        return args[0]
-    return Universe(*args, **kwargs)
-
-
 def Merge(*args):
     """Create a new new :class:`Universe` from one or more
     :class:`~MDAnalysis.core.groups.AtomGroup` instances.
diff --git a/testsuite/MDAnalysisTests/test_api.py b/testsuite/MDAnalysisTests/test_api.py
index 752fb516953..211865db985 100644
--- a/testsuite/MDAnalysisTests/test_api.py
+++ b/testsuite/MDAnalysisTests/test_api.py
@@ -26,23 +26,26 @@
 
 import MDAnalysis as mda
 
+
 def test_Universe():
     assert mda.Universe is mda.core.universe.Universe
 
-def test_as_Universe():
-    assert mda.as_Universe is mda.core.universe.as_Universe
 
 def test_fetch_mmtf():
     assert mda.fetch_mmtf is mda.coordinates.MMTF.fetch_mmtf
 
+
 def test_Writer():
     assert mda.Writer is mda.coordinates.core.writer
 
+
 def test_AtomGroup():
     assert mda.AtomGroup is mda.core.groups.AtomGroup
 
+
 def test_ResidueGroup():
     assert mda.ResidueGroup is mda.core.groups.ResidueGroup
 
+
 def test_SegmentGroup():
     assert mda.SegmentGroup is mda.core.groups.SegmentGroup