diff --git a/galsim/errors.py b/galsim/errors.py
index 01b1be4082..2302b4b2a4 100644
--- a/galsim/errors.py
+++ b/galsim/errors.py
@@ -25,8 +25,8 @@
             'GalSimSEDError', 'GalSimHSMError', 'GalSimFFTSizeError',
             'GalSimConfigError', 'GalSimConfigValueError',
             'GalSimNotImplementedError',
-            'GalSimWarning', 'GalSimDeprecationWarning',
-            'convert_cpp_errors', 'galsim_warn', ]
+            'GalSimWarning', 'GalSimDeprecationWarning', 'GalSimFFTSizeWarning',
+            'convert_cpp_errors', 'galsim_warn', 'galsim_warn_fft' ]
 
 import warnings
 from contextlib import contextmanager
@@ -125,10 +125,6 @@
 # GalSimHSMError:       Use this for errors from the HSM algorithm.  They are emitted in C++, but
 #                       we use `with convert_cpp_errors(GalSimHSMError):` to convert them.
 #
-# GalSimFFTSizeError:   Use this when a requested FFT would exceed the relevant maximum_fft_size
-#                       for the object, so the recommendation is raise this parameter if that
-#                       is possible.
-#
 # GalSimConfigError:    Use this for errors processing a config dict.
 #
 # GalSimConfigValueError:   Use this when a config dict has a value that is invalid. Basically,
@@ -345,6 +341,9 @@ class GalSimFFTSizeError(GalSimError):
         mem:        The estimated memory that would be required (in GB) for the FFT.
     """
     def __init__(self, message, size):
+        from .deprecated import depr
+        depr(GalSimFFTSizeError, 2.7, '',
+             "Cases that used to raise GalSimFFTSizeError now emit a GalSimFFTSizeWarning instead.")
         self.message = message
         self.size = size
         self.mem = size * size * 24. / 1024**3
@@ -412,6 +411,31 @@ class GalSimDeprecationWarning(GalSimWarning):
     """
     def __repr__(self): return 'galsim.GalSimDeprecationWarning(%r)'%(str(self))
 
+class GalSimFFTSizeWarning(GalSimWarning):
+    """A GalSim-specific warning class indicating that a requested FFT exceeds the relevant
+    maximum_fft_size.
+
+    Attributes:
+        size:       The size that was deemed too large
+        mem:        The estimated memory that would be required (in GB) for the FFT.
+    """
+    def __init__(self, message, size):
+        self.message = message
+        self.size = size
+        self.mem = size * size * 24. / 1024**3
+        message += "\nThe required FFT size would be {0} x {0}, which requires ".format(size)
+        message += "{0:.2f} GB of memory.\n".format(self.mem)
+        message += "If you can handle the large FFT and want to suppress this warning,\n"
+        message += "you may update gsparams.maximum_fft_size."
+        super(GalSimFFTSizeWarning, self).__init__(message)
+    def __repr__(self):
+        return 'galsim.GalSimFFTSizeWarning(%r,%r)'%(self.message, self.size)
+    def __reduce__(self):
+        return GalSimFFTSizeWarning, (self.message, self.size)
+
+def galsim_warn_fft(message, size):
+    warnings.warn(GalSimFFTSizeWarning(message, size))
+
 @contextmanager
 def convert_cpp_errors(error_type=GalSimError):
     try:
diff --git a/galsim/gsobject.py b/galsim/gsobject.py
index 4be5872097..d998d743fb 100644
--- a/galsim/gsobject.py
+++ b/galsim/gsobject.py
@@ -27,7 +27,8 @@
 from .position import _PositionD, _PositionI, Position, parse_pos_args
 from ._utilities import lazy_property
 from .errors import GalSimError, GalSimRangeError, GalSimValueError, GalSimIncompatibleValuesError
-from .errors import GalSimFFTSizeError, GalSimNotImplementedError, convert_cpp_errors, galsim_warn
+from .errors import GalSimNotImplementedError, convert_cpp_errors
+from .errors import galsim_warn, galsim_warn_fft
 from .image import Image, ImageD, ImageF, ImageCD, ImageCF
 from .shear import Shear, _Shear
 from .angle import Angle
@@ -162,17 +163,11 @@ class GSObject:
         >>> conv = galsim.Convolve([gal,psf])
         >>> im = galsim.Image(1000,1000, scale=0.02)        # Note the very small pixel scale!
         >>> im = conv.drawImage(image=im)                   # This uses the default GSParams.
-        Traceback (most recent call last):
-          File "<stdin>", line 1, in <module>
-          File "galsim/gsobject.py", line 1666, in drawImage
-            added_photons = prof.drawFFT(draw_image, add)
-          File "galsim/gsobject.py", line 1877, in drawFFT
-            kimage, wrap_size = self.drawFFT_makeKImage(image)
-          File "galsim/gsobject.py", line 1802, in drawFFT_makeKImage
-            raise GalSimFFTSizeError("drawFFT requires an FFT that is too large.", Nk)
-        galsim.errors.GalSimFFTSizeError: drawFFT requires an FFT that is too large.
+        galsim/errors.py:437: GalSimFFTSizeWarning: drawFFT requires a very large FFT.
         The required FFT size would be 12288 x 12288, which requires 3.38 GB of memory.
-        If you can handle the large FFT, you may update gsparams.maximum_fft_size.
+        If you can handle the large FFT and want to suppress this warning,
+        you may update gsparams.maximum_fft_size.
+          warnings.warn(GalSimFFTSizeWarning(message, size))
         >>> big_fft_params = galsim.GSParams(maximum_fft_size=12300)
         >>> conv = galsim.Convolve([gal,psf],gsparams=big_fft_params)
         >>> im = conv.drawImage(image=im)                   # Now it works (but is slow!)
@@ -1968,7 +1963,7 @@ def drawFFT_makeKImage(self, image):
             Nk = int(np.ceil(maxk/dk)) * 2
 
         if Nk > self.gsparams.maximum_fft_size:
-            raise GalSimFFTSizeError("drawFFT requires an FFT that is too large.", Nk)
+            galsim_warn_fft("drawFFT requires a very large FFT.", Nk)
 
         bounds = _BoundsI(0,Nk//2,-Nk//2,Nk//2)
         if image.dtype in (np.complex128, np.float64, np.int32, np.uint32):
diff --git a/galsim/gsparams.py b/galsim/gsparams.py
index f032083652..64f10868ee 100644
--- a/galsim/gsparams.py
+++ b/galsim/gsparams.py
@@ -43,14 +43,16 @@ class GSParams:
     Parameters:
         minimum_fft_size:   The minimum size of any FFT that may need to be performed.
                             [default: 128]
-        maximum_fft_size:   The maximum allowed size of an image for performing an FFT.  This
-                            is more about memory use than accuracy.  We have this maximum
-                            value to help prevent the user from accidentally trying to perform
-                            an extremely large FFT that crashes the program. Instead, GalSim
-                            will raise an exception indicating that the image is too large,
-                            which is often a sign of an error in the user's code. However, if
-                            you have the memory to handle it, you can raise this limit to
-                            allow the calculation to happen. [default: 8192]
+        maximum_fft_size:   The maximum allowed size of an image for performing an FFT without
+                            warning.  This is more about memory use than accuracy.  We have this
+                            maximum value to inform a user who accidentally performs an extremely
+                            large FFT why they just crashed the program. GalSim used to
+                            raise an exception indicating that the image is too large,
+                            which is often a sign of an error in the user's code. However, we
+                            now just emit a warning about the large FFT, so if the code crashes
+                            you have some indication of why. If you have the memory to handle it,
+                            you can raise this limit to allow the calculation to happen without
+                            seeing the warning. [default: 8192]
         folding_threshold:  This sets a maximum amount of real space folding that is allowed,
                             an effect caused by the periodic nature of FFTs.  FFTs implicitly
                             use periodic boundary conditions, and a profile specified on a
diff --git a/galsim/phase_psf.py b/galsim/phase_psf.py
index 003881ba45..e1181f8bf8 100644
--- a/galsim/phase_psf.py
+++ b/galsim/phase_psf.py
@@ -34,7 +34,7 @@
 from .interpolatedimage import InterpolatedImage
 from .utilities import doc_inherit, OrderedWeakRef, rotate_xy, lazy_property, basestring
 from .errors import GalSimValueError, GalSimRangeError, GalSimIncompatibleValuesError
-from .errors import GalSimFFTSizeError, galsim_warn
+from .errors import galsim_warn, galsim_warn_fft
 from .photon_array import TimeSampler, PhotonArray
 from .airy import Airy
 from .second_kick import SecondKick
@@ -328,7 +328,7 @@ def _generate_pupil_plane(self):
 
         # Check FFT size
         if self._npix > self.gsparams.maximum_fft_size:
-            raise GalSimFFTSizeError("Created pupil plane array that is too large.",self._npix)
+            galsim_warn_fft("Created pupil plane array that will need a very large fft.",self._npix)
 
         # Shrink scale such that size = scale * npix exactly.
         self._pupil_plane_scale = self._pupil_plane_size / self._npix
@@ -383,7 +383,7 @@ def _load_pupil_plane(self):
 
         # Check FFT size
         if self._npix > self.gsparams.maximum_fft_size:
-            raise GalSimFFTSizeError("Loaded pupil plane array that is too large.", self._npix)
+            galsim_warn_fft("Loaded pupil plane array that will need a very large fft.",self._npix)
 
         # Sanity checks
         if self._pupil_plane_im.array.shape[0] != self._pupil_plane_im.array.shape[1]:
diff --git a/tests/test_chromatic.py b/tests/test_chromatic.py
index 4eccb9a4a6..4c1603e080 100644
--- a/tests/test_chromatic.py
+++ b/tests/test_chromatic.py
@@ -1493,7 +1493,7 @@ def test_gsparams():
     # getting properly forwarded through the internals of ChromaticObjects.
     gsparams = galsim.GSParams(maximum_fft_size=16)
     gal = galsim.Gaussian(fwhm=1, gsparams=gsparams) * bulge_SED
-    with assert_raises(galsim.GalSimFFTSizeError):
+    with assert_warns(galsim.GalSimFFTSizeWarning):
         gal.drawImage(bandpass)
     assert (galsim.Gaussian(fwhm=1) * bulge_SED) != gal
     assert (galsim.Gaussian(fwhm=1) * bulge_SED).withGSParams(gsparams) == gal
@@ -1503,7 +1503,7 @@ def test_gsparams():
     gal = galsim.Gaussian(fwhm=1) * bulge_SED
     psf = galsim.Gaussian(sigma=0.4)
     final = galsim.Convolve([gal, psf], gsparams=gsparams)
-    with assert_raises(galsim.GalSimFFTSizeError):
+    with assert_warns(galsim.GalSimFFTSizeWarning):
         final.drawImage(bandpass)
 
     # Use a restrictive one this time, so we test the "most restrictive gsparams" feature
diff --git a/tests/test_config_gsobject.py b/tests/test_config_gsobject.py
index 6eba44ee8a..bec54a181b 100644
--- a/tests/test_config_gsobject.py
+++ b/tests/test_config_gsobject.py
@@ -669,7 +669,7 @@ def test_sersic():
     # and would be rather slow.
     gal6a = galsim.config.BuildGSObject(config, 'gal6')[0]
     gal6b = galsim.Sersic(n=0.7, half_light_radius=1, flux=50)
-    with assert_raises(galsim.GalSimFFTSizeError):
+    with assert_warns(galsim.GalSimFFTSizeWarning):
         gsobject_compare(gal6a, gal6b, conv=galsim.Gaussian(sigma=1))
 
     gal7a = galsim.config.BuildGSObject(config, 'gal7')[0]
diff --git a/tests/test_deprecated.py b/tests/test_deprecated.py
index ea7141914a..6f921a948d 100644
--- a/tests/test_deprecated.py
+++ b/tests/test_deprecated.py
@@ -17,6 +17,7 @@
 #
 
 import os
+import warnings
 import numpy as np
 
 import galsim
@@ -968,6 +969,27 @@ def test_save_photons():
         assert np.allclose(np.sum(image.photons.flux), flux, rtol=0.1)
         repr(obj)
 
+@timer
+def test_galsim_fft_size_error():
+    """Test basic usage of GalSimFFTSizeError
+    """
+    # This feela a little gratuitous, since almost certainly no one used GalSimFFTSizeError
+    # for anything directly.  Even catching it seems unlikely.  But it was technically part
+    # of our API, so just deprecate it and make sure it still works appropriately.
+    err = check_dep(galsim.GalSimFFTSizeError, "Test FFT is too big.", 10240)
+    print('str = ',str(err))
+    print('repr = ',repr(err))
+    assert str(err) == ("Test FFT is too big.\nThe required FFT size would be 10240 x 10240, "
+                        "which requires 2.34 GB of memory.\nIf you can handle "
+                        "the large FFT, you may update gsparams.maximum_fft_size.")
+    assert err.size == 10240
+    np.testing.assert_almost_equal(err.mem, 2.34375)
+    assert isinstance(err, galsim.GalSimError)
+    with warnings.catch_warnings():
+        warnings.filterwarnings("ignore",category=galsim.GalSimDeprecationWarning)
+        check_pickle(err)
+
+
 
 if __name__ == "__main__":
     runtests(__file__)
diff --git a/tests/test_errors.py b/tests/test_errors.py
index f407857aed..7d75f0e4f8 100644
--- a/tests/test_errors.py
+++ b/tests/test_errors.py
@@ -203,21 +203,6 @@ def test_galsim_hsm_error():
     check_pickle(err)
 
 
-@timer
-def test_galsim_fft_size_error():
-    """Test basic usage of GalSimFFTSizeError
-    """
-    err = galsim.GalSimFFTSizeError("Test FFT is too big.", 10240)
-    print('str = ',str(err))
-    print('repr = ',repr(err))
-    assert str(err) == ("Test FFT is too big.\nThe required FFT size would be 10240 x 10240, "
-                        "which requires 2.34 GB of memory.\nIf you can handle "
-                        "the large FFT, you may update gsparams.maximum_fft_size.")
-    assert err.size == 10240
-    np.testing.assert_almost_equal(err.mem, 2.34375)
-    assert isinstance(err, galsim.GalSimError)
-    check_pickle(err)
-
 
 @timer
 def test_galsim_config_error():
@@ -296,6 +281,17 @@ def test_galsim_deprecation_warning():
     assert isinstance(err, UserWarning)
     check_pickle(err)
 
+@timer
+def test_galsim_fftsize_warning():
+    """Test basic usage of GalSimFFTSizeWarning
+    """
+    err = galsim.GalSimFFTSizeWarning("Test", 10240)
+    print('str = ',str(err))
+    print('repr = ',repr(err))
+    assert str(err).startswith("Test")
+    assert isinstance(err, UserWarning)
+    check_pickle(err)
+
 
 if __name__ == "__main__":
     runtests(__file__)
diff --git a/tests/test_phase_psf.py b/tests/test_phase_psf.py
index 78bac176ca..658feb2e92 100644
--- a/tests/test_phase_psf.py
+++ b/tests/test_phase_psf.py
@@ -79,18 +79,20 @@ def test_aperture():
         np.testing.assert_almost_equal(stepk, 2.*np.pi/size)
         np.testing.assert_almost_equal(maxk, np.pi/scale)
 
-    # If the constructed pupil plane would be too large, raise an error
-    with assert_raises(galsim.GalSimFFTSizeError):
-        ap = galsim.Aperture(1.7, pupil_plane_scale=1.e-4)
+    # If the constructed pupil plane would be too large, emit a warning
+    # For testing this and the next one, we change gsparams.maximum_fft_size, rather than try
+    # to build or load a really large image.
+    with assert_warns(galsim.GalSimFFTSizeWarning):
+        ap = galsim.Aperture(1.7, pupil_plane_scale=0.01,
+                             gsparams=galsim.GSParams(maximum_fft_size=64))
         ap._illuminated  # Only triggers once we force it to build the illuminated array
 
     # Similar if the given image is too large.
-    # Here, we change gsparams.maximum_fft_size, rather than build a really large image to load.
-    with assert_raises(galsim.GalSimFFTSizeError):
+    with assert_warns(galsim.GalSimFFTSizeWarning):
         ap = galsim.Aperture(1.7, pupil_plane_im=im, gsparams=galsim.GSParams(maximum_fft_size=64))
         ap._illuminated
 
-    # Other choices just give warnings about pupil scale or size being inappropriate
+    # Other choices give warnings about pupil scale or size being inappropriate
     with assert_warns(galsim.GalSimWarning):
         ap = galsim.Aperture(diam=1.7, pupil_plane_size=3, pupil_plane_scale=0.03)
         ap._illuminated
@@ -1537,8 +1539,8 @@ def test_t_persistence():
     nphot = 1_000_000
     photons = psf.drawImage(save_photons=True, method='phot', n_photons=nphot).photons
     assert photons.hasAllocatedTimes()
-    assert np.min(photons.time) > 10.0
-    assert np.max(photons.time) < 25.0
+    assert np.min(photons.time) >= 10.0
+    assert np.max(photons.time) <= 25.0 + 1.e-10  # slight slop to allow for numerical imprecision
 
 
 @timer