diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml
index caad5f8a7..4c1324241 100644
--- a/.pre-commit-config.yaml
+++ b/.pre-commit-config.yaml
@@ -2,7 +2,7 @@ exclude: 'versioneer.py|lmfit/_version|doc/conf.py'
 
 repos:
 -   repo: https://github.com/asottile/pyupgrade
-    rev: v1.22.1
+    rev: v1.23.0
     hooks:
     -   id: pyupgrade
         # for now don't force to change from %-operator to {}
diff --git a/doc/whatsnew.rst b/doc/whatsnew.rst
index 6bfb41534..c0d9bb61d 100644
--- a/doc/whatsnew.rst
+++ b/doc/whatsnew.rst
@@ -41,8 +41,10 @@ Various:
   (replaced by omit) deprecated since 0.9 (PR #565).
 - deprecate 'report_errors' in printfuncs.py (PR #571)
 - updates to the documentation to use ``jupyter-sphinx`` to include examples/output (PRs #573 and #575)
-- include a Gallery with examples in the documentation using ``sphinx-gallery`` (PR #574)
-- improve test-coverage (PRs #571 and #572)
+- include a Gallery with examples in the documentation using ``sphinx-gallery`` (PR #574 and #583)
+- improve test-coverage (PRs #571, #572 and #585)
+- add/clarify warning messages when NaN values are detected (PR #586)
+- several updates to docstrings (Issue #584; PR #583, and others)
 - update pre-commit hooks and several docstrings
 
 .. _whatsnew_0913_label:
diff --git a/lmfit/minimizer.py b/lmfit/minimizer.py
index f26cf5fc2..a4034a22d 100644
--- a/lmfit/minimizer.py
+++ b/lmfit/minimizer.py
@@ -2305,7 +2305,11 @@ def _nan_policy(arr, nan_policy='raise', handle_inf=True):
                           "NaNs will be ignored.", RuntimeWarning)
 
         if contains_nan:
-            raise ValueError("The input contains nan values")
+            msg = ('NaN values detected in your input data or the output of '
+                   'your objective/model function - fitting algorithms cannot '
+                   'handle this! Please read https://lmfit.github.io/lmfit-py/faq.html#i-get-errors-from-nan-in-my-fit-what-can-i-do '
+                   'for more information.')
+            raise ValueError(msg)
     return arr
 
 
diff --git a/lmfit/model.py b/lmfit/model.py
index 653e9cce6..07a5367ab 100644
--- a/lmfit/model.py
+++ b/lmfit/model.py
@@ -757,7 +757,15 @@ def _residual(self, params, data, weights, **kwargs):
         The "ravels" throughout are necessary to support pandas.Series.
 
         """
-        diff = self.eval(params, **kwargs) - data
+        model = self.eval(params, **kwargs)
+        if self.nan_policy == 'raise' and not np.all(np.isfinite(model)):
+            msg = ('The model function generated NaN values and the fit '
+                   'aborted! Please check your model function and/or set '
+                   'boundaries on parameters where applicable. In cases like '
+                   'this, using "nan_policy=\'omit\'" will probably not work.')
+            raise ValueError(msg)
+
+        diff = model - data
 
         if diff.dtype == np.complex:
             # data/model are complex
diff --git a/tests/test_model.py b/tests/test_model.py
index 76288f170..4518e5870 100644
--- a/tests/test_model.py
+++ b/tests/test_model.py
@@ -622,6 +622,7 @@ def gauss(x, sigma, mu, A):
         self.assertTrue(result.params['pos_delta'].value > 0)
 
     def test_model_nan_policy(self):
+        """Tests for nan_policy with NaN values in the input data."""
         x = np.linspace(0, 10, 201)
         np.random.seed(0)
         y = gaussian(x, 10.0, 6.15, 0.8)
@@ -629,6 +630,7 @@ def test_model_nan_policy(self):
         y += gaussian(x, 0.25, 6.00, 7.5)
         y += np.random.normal(size=len(x), scale=0.5)
 
+        # with NaN values in the input data
         y[55] = y[91] = np.nan
         mod = PseudoVoigtModel()
         params = mod.make_params(amplitude=20, center=5.5,
@@ -637,7 +639,9 @@ def test_model_nan_policy(self):
 
         # with raise, should get a ValueError
         result = lambda: mod.fit(y, params, x=x, nan_policy='raise')
-        self.assertRaises(ValueError, result)
+        msg = ('NaN values detected in your input data or the output of your '
+               'objective/model function - fitting algorithms cannot handle this!')
+        self.assertRaisesRegexp(ValueError, msg, result)
 
         # with propagate, should get no error, but bad results
         result = mod.fit(y, params, x=x, nan_policy='propagate')
@@ -663,6 +667,25 @@ def test_model_nan_policy(self):
         with pytest.raises(ValueError, match=err_msg):
             mod.fit(y, params, x=x, nan_policy='wrong_argument')
 
+    def test_model_nan_policy_NaNs_by_model(self):
+        """Test for nan_policy with NaN values generated by the model function."""
+        def double_exp(x, a1, t1, a2, t2):
+            return a1*np.exp(-x/t1) + a2*np.exp(-(x-0.1) / t2)
+
+        model = Model(double_exp)
+
+        truths = (3.0, 2.0, -5.0, 10.0)
+        x = np.linspace(1, 10, 250)
+        np.random.seed(0)
+        y = double_exp(x, *truths) + 0.1*np.random.randn(x.size)
+
+        p = model.make_params(a1=4, t1=3, a2=4, t2=3)
+        result = lambda: model.fit(data=y, params=p, x=x, method='Nelder',
+                                   nan_policy='raise')
+
+        msg = 'The model function generated NaN values and the fit aborted!'
+        self.assertRaisesRegexp(ValueError, msg, result)
+
     @pytest.mark.skipif(sys.version_info.major == 2,
                         reason="cannot use wrapped functions with Python 2")
     def test_wrapped_model_func(self):