diff --git a/astropy/wcs/wcsapi/fitswcs.py b/astropy/wcs/wcsapi/fitswcs.py
index 58705d1865ac..47ef8f7b3e10 100644
--- a/astropy/wcs/wcsapi/fitswcs.py
+++ b/astropy/wcs/wcsapi/fitswcs.py
@@ -401,7 +401,12 @@ def _get_components_and_classes(self):
 
                 kwargs = {}
                 kwargs['frame'] = celestial_frame
-                kwargs['unit'] = u.deg
+                # Very occasionally (TAB) wcs does not convert the units
+                # We call set here to make sure any unit conversion which is
+                # going to happen has been done.
+                self.wcs.set()
+                kwargs['unit'] = (u.Unit(self.wcs.cunit[self.wcs.lng]),
+                                  u.Unit(self.wcs.cunit[self.wcs.lat]))
 
                 classes['celestial'] = (SkyCoord, (), kwargs)
 
@@ -431,7 +436,7 @@ def _get_components_and_classes(self):
                 earth_location = EarthLocation(*self.wcs.obsgeo[:3], unit=u.m)
 
                 # Get the time scale from TIMESYS or fall back to 'utc'
-                tscale = self.wcs.timesys or 'utc'
+                tscale = self.wcs.timesys.lower() or 'utc'
 
                 if np.isnan(self.wcs.mjdavg):
                     obstime = Time(self.wcs.mjdobs, format='mjd', scale=tscale,
@@ -630,8 +635,8 @@ def value_from_spectralcoord(spectralcoord):
                     # Initialize delta
                     reference_time_delta = None
 
-                    # Extract time scale
-                    scale = self.wcs.ctype[i].lower()
+                    # Extract time scale, and remove any algorithm code
+                    scale = self.wcs.ctype[i].split("-")[0].lower()
 
                     if scale == 'time':
                         if self.wcs.timesys: