diff --git a/doc/fp_utilities/ulps_plots.qbk b/doc/fp_utilities/ulps_plots.qbk
index 76d8e03539..3a6eca5bda 100644
--- a/doc/fp_utilities/ulps_plots.qbk
+++ b/doc/fp_utilities/ulps_plots.qbk
@@ -18,32 +18,60 @@
     public:
         ulps_plot(F hi_acc_impl, CoarseReal a, CoarseReal b,
                   size_t samples = 10000, bool perturb_abscissas = false, int random_seed = -1);
-
+        //
+        // Set a clip value to restrict the range of ULP's shown, values outside [-clip,clip]
+        // will be shown at the clip boundary and in a different color (red by default):
+        //
         ulps_plot& clip(PreciseReal clip);
-
+        //
+        // The width of the SVG:
+        //
         ulps_plot& width(int width);
-
+        //
+        // The color of the condition number envelope:
+        //
         ulps_plot& envelope_color(std::string const & color);
-
+        //
+        // Title:
+        //
         ulps_plot& title(std::string const & title);
-
+        //
+        // Background color:
+        //
         ulps_plot& background_color(std::string const & background_color);
-
+        //
+        // Font color:
+        //
         ulps_plot& font_color(std::string const & font_color);
-
+        //
+        // Sets the color of points which are cropped, or set to an empty
+        // string to hide them completely (default is "red"):
+        //
+        ulps_plot& crop_color(std::string const & font_color);
+        //
+        // Set's the color of points where one of the functions returned a NaN,
+        // or set to an empty string to hide completely (the default):
+        //
+        ulps_plot& nan_color(std::string const & font_color);
+        //
+        // Show ULP envelope true/false:
+        //
         ulps_plot& ulp_envelope(bool write_ulp);
-
+        //
+        // The number of horizontal/vertical lines to draw:
+        //
         ulps_plot& horizontal_lines(int horizontal_lines);
-
         ulps_plot& vertical_lines(int vertical_lines);
-
+        //
+        // Add a function, and plot color:
+        //
         template<class G>
         ulps_plot& add_fn(G g, std::string const & color = "steelblue");
-
+        //
+        // Write to stream or file:
+        //
         friend std::ostream& operator<<(std::ostream& fs, ulps_plot const & plot)
-
         void write(std::string const & filename) const;
-
     };
     
     } // namespaces
diff --git a/include/boost/math/tools/ulps_plot.hpp b/include/boost/math/tools/ulps_plot.hpp
index 9a1e004ee8..3d941f4445 100644
--- a/include/boost/math/tools/ulps_plot.hpp
+++ b/include/boost/math/tools/ulps_plot.hpp
@@ -79,6 +79,10 @@ class ulps_plot {
 
     ulps_plot& font_color(std::string const & font_color);
 
+    ulps_plot& crop_color(std::string const & color);
+
+    ulps_plot& nan_color(std::string const & color);
+
     ulps_plot& ulp_envelope(bool write_ulp);
 
     template<class G>
@@ -243,15 +247,28 @@ class ulps_plot {
             {
                 if (isnan(ulp[j]))
                 {
-                    continue;
+                    if(plot.nan_color_ == "")
+                        continue;
+                    CoarseReal x = x_scale(plot.coarse_abscissas_[j]);
+                    PreciseReal y = y_scale(static_cast<PreciseReal>(plot.clip_));
+                    fs << "<circle cx='" << x << "' cy='" << y << "' r='1' fill='" << plot.nan_color_ << "'/>\n";
+                    y = y_scale(static_cast<PreciseReal>(-plot.clip_));
+                    fs << "<circle cx='" << x << "' cy='" << y << "' r='1' fill='" << plot.nan_color_ << "'/>\n";
                 }
                 if (plot.clip_ > 0 && static_cast<PreciseReal>(abs(ulp[j])) > plot.clip_)
                 {
-                    continue;
+                   if (plot.crop_color_ == "")
+                      continue;
+                   CoarseReal x = x_scale(plot.coarse_abscissas_[j]);
+                   PreciseReal y = y_scale(static_cast<PreciseReal>(ulp[j] < 0 ? -plot.clip_ : plot.clip_));
+                   fs << "<circle cx='" << x << "' cy='" << y << "' r='1' fill='" << plot.crop_color_ << "'/>\n";
+                }
+                else
+                {
+                   CoarseReal x = x_scale(plot.coarse_abscissas_[j]);
+                   PreciseReal y = y_scale(static_cast<PreciseReal>(ulp[j]));
+                   fs << "<circle cx='" << x << "' cy='" << y << "' r='1' fill='" << color << "'/>\n";
                 }
-                CoarseReal x = x_scale(plot.coarse_abscissas_[j]);
-                PreciseReal y = y_scale(static_cast<PreciseReal>(ulp[j]));
-                fs << "<circle cx='" << x << "' cy='" << y << "' r='1' fill='" << color << "'/>\n";
             }
         }
 
@@ -351,6 +368,8 @@ class ulps_plot {
     std::string title_;
     std::string background_color_;
     std::string font_color_;
+    std::string crop_color_;
+    std::string nan_color_;
 };
 
 template<class F, typename PreciseReal, typename CoarseReal>
@@ -409,6 +428,20 @@ ulps_plot<F, PreciseReal, CoarseReal>& ulps_plot<F, PreciseReal, CoarseReal>::fo
     return *this;
 }
 
+template<class F, typename PreciseReal, typename CoarseReal>
+ulps_plot<F, PreciseReal, CoarseReal>& ulps_plot<F, PreciseReal, CoarseReal>::crop_color(std::string const & color)
+{
+    crop_color_ = color;
+    return *this;
+}
+
+template<class F, typename PreciseReal, typename CoarseReal>
+ulps_plot<F, PreciseReal, CoarseReal>& ulps_plot<F, PreciseReal, CoarseReal>::nan_color(std::string const & color)
+{
+    nan_color_ = color;
+    return *this;
+}
+
 template<class F, typename PreciseReal, typename CoarseReal>
 ulps_plot<F, PreciseReal, CoarseReal>& ulps_plot<F, PreciseReal, CoarseReal>::ulp_envelope(bool write_ulp_envelope)
 {
@@ -431,11 +464,10 @@ void ulps_plot<F, PreciseReal, CoarseReal>::write(std::string const & filename)
 
 template<class F, typename PreciseReal, typename CoarseReal>
 ulps_plot<F, PreciseReal, CoarseReal>::ulps_plot(F hi_acc_impl, CoarseReal a, CoarseReal b,
-             size_t samples, bool perturb_abscissas, int random_seed)
+             size_t samples, bool perturb_abscissas, int random_seed) : crop_color_("red")
 {
-    // This fails for heap allocated types like MPFR.
-    // Got to think on what to do about it.
-    static_assert(sizeof(PreciseReal) >= sizeof(CoarseReal), "PreciseReal must have larger size than CoarseReal");
+    // Use digits10 for this comparison in case the two types have differeing radixes:
+    static_assert(std::numeric_limits<PreciseReal>::digits10 >= std::numeric_limits<CoarseReal>::digits10, "PreciseReal must have higher precision that CoarseReal");
     if (samples < 10)
     {
         throw std::domain_error("Must have at least 10 samples, samples = " + std::to_string(samples));