diff --git a/prospect/models/__init__.py b/prospect/models/__init__.py
index 1fe98241..728647e8 100644
--- a/prospect/models/__init__.py
+++ b/prospect/models/__init__.py
@@ -6,14 +6,13 @@
 """
 
 
-from .sedmodel import ProspectorParams, SpecModel
-from .sedmodel import PolySpecModel, SplineSpecModel
-from .sedmodel import AGNSpecModel
+from .parameters import ProspectorParams
+from .sedmodel import SpecModel, HyperSpecModel, AGNSpecModel
 
 
 __all__ = ["ProspectorParams",
            "SpecModel",
-           "PolySpecModel", "SplineSpecModel",
-           "LineSpecModel", "AGNSpecModel"
+           "HyperSpecModel",
+           "AGNSpecModel"
            ]
 
diff --git a/prospect/models/sedmodel.py b/prospect/models/sedmodel.py
index b3983731..b7e73477 100644
--- a/prospect/models/sedmodel.py
+++ b/prospect/models/sedmodel.py
@@ -22,10 +22,8 @@
 
 
 __all__ = ["SpecModel",
-           "PolySpecModel", "SplineSpecModel",
-           "HyperSpecModel", "HyperPolySpecModel",
-           "AGNSpecModel",
-           "PolyFitModel"]
+           "HyperSpecModel",
+           "AGNSpecModel"]
 
 
 class SpecModel(ProspectorParams):
@@ -103,7 +101,28 @@ def predict(self, theta, observations=None, sps=None, **extras):
             will be `mfrac` the ratio of the surviving stellar mass to the
             stellar mass formed.
         """
+        self.predict_init(theta, sps)
 
+        # generate predictions for likelihood
+        # this assumes all spectral datasets (if present) occur first
+        # because they can change the line strengths during marginalization.
+        predictions = [self.predict_obs(obs) for obs in observations]
+
+        return predictions, self._mfrac
+
+    def predict_init(self, theta, sps):
+        """Generate the physical model on the model wavelength grid, and cache
+        many quantities used in common for all kinds of predictions.
+
+        Parameters
+        ----------
+        theta : ndarray of shape ``(ndim,)``
+            Vector of free model parameter values.
+
+        sps :
+            An `sps` object to be used in the model generation.  It must have
+            the :py:func:`get_galaxy_spectrum` method defined.
+        """
         # generate and cache intrinsic model spectrum and info
         self.set_parameters(theta)
         self._wave, self._spec, self._mfrac = sps.get_galaxy_spectrum(**self.params)
@@ -131,13 +150,6 @@ def predict(self, theta, observations=None, sps=None, **extras):
         self._smooth_spec = self.add_dla(self._wave, self._smooth_spec)
         self._smooth_spec = self.add_damping_wing(self._wave, self._smooth_spec)
 
-        # generate predictions for likelihood
-        # this assumes all spectral datasets (if present) occur first
-        # because they can change the line strengths during marginalization.
-        predictions = [self.predict_obs(obs) for obs in observations]
-
-        return predictions, self._mfrac
-
     def predict_obs(self, obs):
         if obs.kind == "spectrum":
             prediction = self.predict_spec(obs)
@@ -253,6 +265,7 @@ def predict_spec(self, obs):
         obs_wave = self.observed_wave(self._wave, do_wavecal=False)
 
         # get output wavelength vector
+        # TODO: remove this and require all Spectrum instances to have a wavelength array
         self._outwave = obs.wavelength
         if self._outwave is None:
             self._outwave = obs_wave
@@ -285,15 +298,19 @@ def predict_spec(self, obs):
             inst_spec[emask] += self._fix_eline_spec.sum(axis=1)
 
         # --- (de-) apply calibration ---
+        extra_mask = self._fit_eline_pixelmask
+        if not extra_mask.any():
+            extra_mask = True  # all pixels are ok
         response = obs.compute_response(spec=inst_spec,
-                                        extra_mask=self._fit_eline_pixelmask,
+                                        extra_mask=extra_mask,
                                         **self.params)
         inst_spec = inst_spec * response
 
         # --- fit and add lines if necessary ---
         emask = self._fit_eline_pixelmask
         if emask.any():
-            # We need the spectroscopic covariance matrix to do emission line optimization and marginalization
+            # We need the spectroscopic covariance matrix to do emission line
+            # optimization and marginalization
             spec_unc = None
             # FIXME: do this only if the noise model is non-trivial, and make sure masking is consistent
             #vectors = obs.noise.populate_vectors(obs)
@@ -302,7 +319,8 @@ def predict_spec(self, obs):
             inst_spec[emask] += self._fit_eline_spec.sum(axis=1)
 
         # --- cache intrinsic spectrum for this observation ---
-        self._sed.append(inst_spec / response)
+        self._sed = inst_spec / response
+        self._speccal = response
 
         return inst_spec
 
@@ -635,6 +653,7 @@ def fit_mle_elines(self, obs, calibrated_spec, sigma_spec=None):
 
         # generate line amplitudes in observed flux units
         units_factor = self.flux_norm() / (1 + self._zred)
+        # FIXME: use obs.response instead of _speccal, remove all references to speccal
         calib_factor = np.interp(self._ewave_obs[idx], nebwave, self._speccal[emask])
         linecal = units_factor * calib_factor
         alpha_breve = self._eline_lum[idx] * linecal
@@ -959,6 +978,7 @@ def predict_spec(self, obs):
 
         # --- cache intrinsic spectrum ---
         self._sed = inst_spec / response
+        self._speccal = response
 
         return inst_spec
 
diff --git a/prospect/observation/__init__.py b/prospect/observation/__init__.py
index 282e93c6..46bf1ef4 100644
--- a/prospect/observation/__init__.py
+++ b/prospect/observation/__init__.py
@@ -1,10 +1,13 @@
 # -*- coding: utf-8 -*-
 
 from .observation import Observation
-from .observation import Photometry, Spectrum, Lines, UndersampledSpectrum, IntrinsicSpectrum
+from .observation import Photometry, Spectrum, Lines
+from .observation import UndersampledSpectrum, IntrinsicSpectrum
+from .observation import PolyOptCal, SplineOptCal
 from .observation import from_oldstyle, from_serial
 
 __all__ = ["Observation",
            "Photometry", "Spectrum", "Lines",
            "UndersampledSpectrum", "InstrinsicSpectrum",
+           "PolyOptCal", "SplineOptCal",
            "from_oldstyle", "from_serial"]
diff --git a/prospect/observation/observation.py b/prospect/observation/observation.py
index 0aa78cc3..58a544ab 100644
--- a/prospect/observation/observation.py
+++ b/prospect/observation/observation.py
@@ -447,7 +447,6 @@ def instrumental_response(self, **extras):
             return 1.0
 
 
-
 class Lines(Spectrum):
 
     _kind = "lines"
@@ -532,10 +531,10 @@ def __init__(self, *args,
                  polynomial_regularization=0,
                  median_polynomial=0,
                  **kwargs):
-        super(PolyOptCal, self).__init(*args, **kwargs)
+        super(PolyOptCal, self).__init__(*args, **kwargs)
         self.polynomial_order = polynomial_order
         self.polynomial_regularization = polynomial_regularization
-        self.median_molynomial = median_polynomial
+        self.median_polynomial = median_polynomial
 
     def _available_parameters(self):
         # These should both be attached to the Observation instance as attributes
@@ -573,7 +572,8 @@ def compute_response(self, spec=None, extra_mask=True, **kwargs):
         assert (self.mask.sum() > order), f"Not enough points to constrain polynomial of order {order}"
 
         polyopt = (order > 0)
-        if ~polyopt:
+        if (not polyopt):
+            print("no polynomial")
             self.response = np.ones_like(self.wavelength)
             return self.response
 
@@ -614,7 +614,7 @@ def __init__(self, *args,
                  spline_knot_spacing=None,
                  spline_knot_n=None,
                  **kwargs):
-        super(SplineOptCal, self).__init(*args, **kwargs)
+        super(SplineOptCal, self).__init__(*args, **kwargs)
 
         self.params = {}
         if spline_knot_wave is not None:
diff --git a/tests/test_polycal.py b/tests/test_polycal.py
new file mode 100644
index 00000000..7a3261c4
--- /dev/null
+++ b/tests/test_polycal.py
@@ -0,0 +1,80 @@
+#!/usr/bin/env python
+# -*- coding: utf-8 -*-
+
+import numpy as np
+import pytest
+
+from prospect.sources import CSPSpecBasis
+from prospect.models import SpecModel, templates
+from prospect.observation import Spectrum, Photometry, PolyOptCal
+
+
+class PolySpectrum(PolyOptCal, Spectrum):
+    pass
+
+
+
+@pytest.fixture
+def get_sps():
+    sps = CSPSpecBasis(zcontinuous=1)
+    return sps
+
+
+def build_model(add_neb=False):
+    model_params = templates.TemplateLibrary["parametric_sfh"]
+    if add_neb:
+        model_params.update(templates.TemplateLibrary["nebular"])
+    return SpecModel(model_params)
+
+
+def build_obs(multispec=False):
+    N = 1500 * (2 - multispec)
+    wmax = 7000
+    wsplit = wmax - N * multispec
+
+    fnames = list([f"sdss_{b}0" for b in "ugriz"])
+    Nf = len(fnames)
+    phot = [Photometry(filters=fnames,
+                       flux=np.ones(Nf),
+                       uncertainty=np.ones(Nf)/10)]
+    spec = [PolySpectrum(wavelength=np.linspace(4000, wsplit, N),
+                         flux=np.ones(N),
+                         uncertainty=np.ones(N) / 10,
+                         mask=slice(None),
+                         polynomial_order=5)
+            ]
+
+    if multispec:
+        spec += [Spectrum(wavelength=np.linspace(wsplit+1, wmax, N),
+                          flux=np.ones(N), uncertainty=np.ones(N) / 10,
+                          mask=slice(None))]
+
+    obslist = spec + phot
+    [obs.rectify() for obs in obslist]
+    return obslist
+
+
+def test_polycal(plot=False):
+    """Make sure the polynomial optimization works
+    """
+    sps = get_sps
+    observations = build_obs()
+    model = build_model()
+
+    preds, extra = model.predict(model.theta, observations=observations, sps=sps)
+    obs = observations[0]
+
+    assert np.any(obs.response != 0)
+
+    if plot:
+        import matplotlib.pyplot as pl
+        fig, axes = pl.subplots(3, 1, sharex=True)
+        ax = axes[0]
+        ax.plot(obs.wavelength, obs.flux, label="obseved flux (ones)")
+        ax.plot(obs.wavelength, preds[0], label="model flux (times response)")
+        ax = axes[1]
+        ax.plot(obs.wavelength, obs.response, label="instrumental response (polynomial)")
+        ax = axes[2]
+        ax.plot(obs.wavelength, preds[0]/ obs.response, label="intrinsic model spectrum")
+        ax.set_xlabel("wavelength")
+        [ax.legend() for ax in axes]
\ No newline at end of file