diff --git a/package/CHANGELOG b/package/CHANGELOG
index 25a6a793a5c..4c9a8fc6861 100644
--- a/package/CHANGELOG
+++ b/package/CHANGELOG
@@ -78,6 +78,8 @@ Enhancements
     convert between a parmed.Structure and MDAnalysis Universe (PR #2404)
 
 Changes
+  * AlignTraj `save()` method has been removed and the `filename` variable now
+    defaults to the current working directory (Issues #2099, #1745, #2443)
   * Removed `MDAnalysis.migration` (Issue #2490, PR #2496)
   * The fasta2select now always assumes that the gap character in a sequence
     is "-" (Issue #2448, PR #2457)
diff --git a/package/MDAnalysis/analysis/align.py b/package/MDAnalysis/analysis/align.py
index 405b39a1b8f..ad0a8f6e35d 100644
--- a/package/MDAnalysis/analysis/align.py
+++ b/package/MDAnalysis/analysis/align.py
@@ -204,7 +204,7 @@
 from MDAnalysis.exceptions import SelectionError, SelectionWarning
 import MDAnalysis.analysis.rms as rms
 from MDAnalysis.coordinates.memory import MemoryReader
-from MDAnalysis.lib.util import get_weights, deprecate
+from MDAnalysis.lib.util import get_weights
 
 from .base import AnalysisBase
 
@@ -536,6 +536,10 @@ class AlignTraj(AnalysisBase):
     `filename`. One can also use the same universe if one wants to fit to the
     current frame.
 
+    .. versionchanged:: 1.0.0
+       ``save()`` has now been removed, as an alternative use ``np.savetxt()``
+       on :attr:`rmsd`.
+
     """
 
     def __init__(self, mobile, reference, select='all', filename=None,
@@ -613,6 +617,9 @@ def __init__(self, mobile, reference, select='all', filename=None,
           already a :class:`MemoryReader` then it is *always* treated as if
           ``in_memory`` had been set to ``True``.
 
+        .. versionchanged:: 1.0.0
+           Default ``filename`` has now been changed to the current directory.
+
         .. deprecated:: 0.19.1
            Default ``filename`` directory will change in 1.0 to the current directory.
 
@@ -635,13 +642,8 @@ def __init__(self, mobile, reference, select='all', filename=None,
             logger.info("Moved mobile trajectory to in-memory representation")
         else:
             if filename is None:
-                # DEPRECATED in 0.19.1
-                # Change in 1.0
-                #
-                # fn = os.path.split(mobile.trajectory.filename)[1]
-                # filename = prefix + fn
-                path, fn = os.path.split(mobile.trajectory.filename)
-                filename = os.path.join(path, prefix + fn)
+                fn = os.path.split(mobile.trajectory.filename)[1]
+                filename = prefix + fn
                 logger.info('filename of rms_align with no filename given'
                             ': {0}'.format(filename))
 
@@ -699,14 +701,6 @@ def _conclude(self):
         if not self._verbose:
             logging.disable(logging.NOTSET)
 
-    @deprecate(release="0.19.0", remove="1.0")
-    def save(self, rmsdfile):
-        """save rmsd as a numpy array
-        """
-        # these are the values of the new rmsd between the aligned trajectory
-        # and reference structure
-        np.savetxt(rmsdfile, self.rmsd)
-        logger.info("Wrote RMSD timeseries  to file %r", rmsdfile)
 
 class AverageStructure(AnalysisBase):
     """RMS-align trajectory to a reference structure using a selection, 
diff --git a/testsuite/MDAnalysisTests/analysis/test_align.py b/testsuite/MDAnalysisTests/analysis/test_align.py
index 56f34f183e7..c8fd4bbf6af 100644
--- a/testsuite/MDAnalysisTests/analysis/test_align.py
+++ b/testsuite/MDAnalysisTests/analysis/test_align.py
@@ -211,8 +211,6 @@ def test_rmsd_custom_weights(self, universe, reference):
         assert_almost_equal(rmsd[1], rmsd_weights[1], 6)
 
     def test_AlignTraj_outfile_default(self, universe, reference):
-        # NOTE: Remove the line os.remove() with release 1.0,
-        #       when the default behavior of AlignTraj changes.
         with tempdir.in_tempdir():
             reference.trajectory[-1]
             x = align.AlignTraj(universe, reference)
@@ -220,7 +218,6 @@ def test_AlignTraj_outfile_default(self, universe, reference):
                 assert os.path.basename(x.filename) == 'rmsfit_adk_dims.dcd'
             finally:
                 x._writer.close()
-                os.remove(x.filename)
 
     def test_AlignTraj_outfile_default_exists(self, universe, reference, tmpdir):
         reference.trajectory[-1]
@@ -250,9 +247,6 @@ def test_AlignTraj(self, universe, reference, tmpdir):
         x = align.AlignTraj(universe, reference, filename=outfile).run()
         fitted = mda.Universe(PSF, outfile)
 
-        rmsd_outfile = str(tmpdir.join('rmsd'))
-        x.save(rmsd_outfile)
-
         assert_almost_equal(x.rmsd[0], 6.9290, decimal=3)
         assert_almost_equal(x.rmsd[-1], 5.2797e-07, decimal=3)
 
@@ -262,11 +256,6 @@ def test_AlignTraj(self, universe, reference, tmpdir):
         self._assert_rmsd(reference, fitted, 0, 6.929083044751061)
         self._assert_rmsd(reference, fitted, -1, 0.0)
 
-        # superficially check saved file rmsd_outfile
-        rmsd = np.loadtxt(rmsd_outfile)
-        assert_array_almost_equal(rmsd, x.rmsd,
-                                  err_msg="saved RMSD not correct")
-
     def test_AlignTraj_weighted(self, universe, reference, tmpdir):
         outfile = str(tmpdir.join('align_test.dcd'))
         x = align.AlignTraj(universe, reference,