diff --git a/src/pyrtools/pyramids/SteerablePyramidFreq.py b/src/pyrtools/pyramids/SteerablePyramidFreq.py
index c05797a..eb6dffc 100644
--- a/src/pyrtools/pyramids/SteerablePyramidFreq.py
+++ b/src/pyrtools/pyramids/SteerablePyramidFreq.py
@@ -20,6 +20,9 @@ class SteerablePyramidFreq(SteerablePyramidBase):
     The squared radial functions tile the Fourier plane with a raised-cosine
     falloff. Angular functions are cos(theta- k*pi/order+1)^(order).
 
+    Note that reconstruction will not be exact if the image has an odd shape (due to
+    boundary-handling issues) or if the pyramid is complex with order=0.
+
     Notes
     -----
     Transform described in [1]_, filter kernel design described in [2]_.
@@ -30,7 +33,7 @@ class SteerablePyramidFreq(SteerablePyramidBase):
         2d image upon which to construct to the pyramid.
     height : 'auto' or `int`.
         The height of the pyramid. If 'auto', will automatically determine based on the size of
-        `image`.
+        `image`. If an int, must be non-negative. When height=0, only returns the residuals.
     order : `int`.
         The Gaussian derivative order used for the steerable filters. Default value is 3.
         Note that to achieve steerability the minimum number of orientation is `order` + 1,
@@ -52,7 +55,8 @@ class SteerablePyramidFreq(SteerablePyramidBase):
         Human-readable string specifying the type of pyramid. For base class, is None.
     pyr_coeffs : `dict`
         Dictionary containing the coefficients of the pyramid. Keys are `(level, band)` tuples and
-        values are 1d or 2d numpy arrays (same number of dimensions as the input image)
+        values are 1d or 2d numpy arrays (same number of dimensions as the input image),
+        running from fine to coarse.
     pyr_size : `dict`
         Dictionary containing the sizes of the pyramid coefficients. Keys are `(level, band)`
         tuples and values are tuples.
@@ -66,6 +70,7 @@ class SteerablePyramidFreq(SteerablePyramidBase):
        Oct 1995.
     .. [2] A Karasaridis and E P Simoncelli, "A Filter Design Technique for Steerable Pyramid
        Image Transforms", ICASSP, Atlanta, GA, May 1996.
+
     """
     def __init__(self, image, height='auto', order=3, twidth=1, is_complex=False):
         # in the Fourier domain, there's only one choice for how do edge-handling: circular. to
@@ -78,24 +83,35 @@ def __init__(self, image, height='auto', order=3, twidth=1, is_complex=False):
         self.filters = {}
         self.order = int(order)
 
+        if (image.shape[0] % 2 != 0) or (image.shape[1] % 2 != 0):
+            warnings.warn("Reconstruction will not be perfect with odd-sized images")
+
+        if self.order == 0 and self.is_complex:
+            raise ValueError(
+                "Complex pyramid cannot have order=0! See "
+                "https://github.com/plenoptic-org/plenoptic/issues/326 "
+                "for an explanation."
+            )
+
         # we can't use the base class's _set_num_scales method because the max height is calculated
         # slightly differently
         max_ht = np.floor(np.log2(min(self.image.shape))) - 2
         if height == 'auto' or height is None:
             self.num_scales = int(max_ht)
         elif height > max_ht:
-            raise Exception("Cannot build pyramid higher than %d levels." % (max_ht))
+            raise ValueError("Cannot build pyramid higher than %d levels." % (max_ht))
+        elif height < 0:
+            raise ValueError("Height must be a non-negative int.")
         else:
             self.num_scales = int(height)
 
         if self.order > 15 or self.order < 0:
-            raise Exception("order must be an integer in the range [0,15]. Truncating.")
+            raise ValueError("order must be an integer in the range [0,15].")
 
         self.num_orientations = int(order + 1)
 
         if twidth <= 0:
-            warnings.warn("twidth must be positive. Setting to 1.")
-            twidth = 1
+            raise ValueError("twidth must be positive.")
         twidth = int(twidth)
 
         dims = np.array(self.image.shape)
@@ -220,8 +236,7 @@ def recon_pyr(self, levels='all', bands='all', twidth=1):
 
         """
         if twidth <= 0:
-            warnings.warn("twidth must be positive. Setting to 1.")
-            twidth = 1
+            raise ValueError("twidth must be positive.")
 
         recon_keys = self._recon_keys(levels, bands)
 
diff --git a/src/pyrtools/pyramids/pyramid.py b/src/pyrtools/pyramids/pyramid.py
index 9670582..5f216e6 100644
--- a/src/pyrtools/pyramids/pyramid.py
+++ b/src/pyrtools/pyramids/pyramid.py
@@ -96,7 +96,7 @@ def _set_num_scales(self, filter_name, height, extra_height=0):
         if height == 'auto':
             self.num_scales = max_ht
         elif height > max_ht:
-            raise Exception("Cannot build pyramid higher than %d levels." % (max_ht))
+            raise ValueError("Cannot build pyramid higher than %d levels." % (max_ht))
         else:
             self.num_scales = int(height)