diff --git a/include/boost/math/special_functions/jacobi_elliptic.hpp b/include/boost/math/special_functions/jacobi_elliptic.hpp
index 114b991d9..149e9fb1c 100644
--- a/include/boost/math/special_functions/jacobi_elliptic.hpp
+++ b/include/boost/math/special_functions/jacobi_elliptic.hpp
@@ -41,9 +41,7 @@ T jacobi_imp(const T& x, const T& k, T* cn, T* dn, const Policy& pol, const char
    BOOST_MATH_STD_USING
    if(k < 0)
    {
-      *cn = policies::raise_domain_error<T>(function, "Modulus k must be positive but got %1%.", k, pol);
-      *dn = *cn;
-      return *cn;
+      return *dn = *cn = policies::raise_domain_error<T>(function, "Modulus k must be positive but got %1%.", k, pol);
    }
    if(k > 1)
    {
diff --git a/test/test_jacobi.hpp b/test/test_jacobi.hpp
index 186def46b..ce2ec9c4e 100644
--- a/test/test_jacobi.hpp
+++ b/test/test_jacobi.hpp
@@ -186,5 +186,33 @@ void test_spots(T, const char* type_name)
     BOOST_CHECK_CLOSE_FRACTION(boost::math::jacobi_sn(T(0.5), T(0.5)), static_cast<T>(0.475082936028536510082218324703870258745078171807428948028252L), tol);
     BOOST_CHECK_CLOSE_FRACTION(boost::math::jacobi_sn(T(0.5), T(0.5), pol), static_cast<T>(0.475082936028536510082218324703870258745078171807428948028252L), tol);
 
+    //
+    // Bug cases and coverage:
+    //
+#ifndef BOOST_MATH_NO_EXCEPTIONS
+    BOOST_CHECK_THROW(boost::math::jacobi_cd(T(-0.5), T(0.5)), std::domain_error);
+    BOOST_CHECK_THROW(boost::math::jacobi_cn(T(-0.5), T(0.5)), std::domain_error);
+    BOOST_CHECK_THROW(boost::math::jacobi_cs(T(-0.5), T(0.5)), std::domain_error);
+    BOOST_CHECK_THROW(boost::math::jacobi_dn(T(-0.5), T(0.5)), std::domain_error);
+    BOOST_CHECK_THROW(boost::math::jacobi_ds(T(-0.5), T(0.5)), std::domain_error);
+    BOOST_CHECK_THROW(boost::math::jacobi_nc(T(-0.5), T(0.5)), std::domain_error);
+    BOOST_CHECK_THROW(boost::math::jacobi_nd(T(-0.5), T(0.5)), std::domain_error);
+    BOOST_CHECK_THROW(boost::math::jacobi_ns(T(-0.5), T(0.5)), std::domain_error);
+    BOOST_CHECK_THROW(boost::math::jacobi_sc(T(-0.5), T(0.5)), std::domain_error);
+    BOOST_CHECK_THROW(boost::math::jacobi_sd(T(-0.5), T(0.5)), std::domain_error);
+    BOOST_CHECK_THROW(boost::math::jacobi_sn(T(-0.5), T(0.5)), std::domain_error);
+#else
+    BOOST_CHECK((boost::math::isnan)(boost::math::jacobi_cd(T(-0.5), T(0.5))));
+    BOOST_CHECK((boost::math::isnan)(boost::math::jacobi_cn(T(-0.5), T(0.5))));
+    BOOST_CHECK((boost::math::isnan)(boost::math::jacobi_cs(T(-0.5), T(0.5))));
+    BOOST_CHECK((boost::math::isnan)(boost::math::jacobi_dn(T(-0.5), T(0.5))));
+    BOOST_CHECK((boost::math::isnan)(boost::math::jacobi_ds(T(-0.5), T(0.5))));
+    BOOST_CHECK((boost::math::isnan)(boost::math::jacobi_nc(T(-0.5), T(0.5))));
+    BOOST_CHECK((boost::math::isnan)(boost::math::jacobi_nd(T(-0.5), T(0.5))));
+    BOOST_CHECK((boost::math::isnan)(boost::math::jacobi_ns(T(-0.5), T(0.5))));
+    BOOST_CHECK((boost::math::isnan)(boost::math::jacobi_sc(T(-0.5), T(0.5))));
+    BOOST_CHECK((boost::math::isnan)(boost::math::jacobi_sd(T(-0.5), T(0.5))));
+    BOOST_CHECK((boost::math::isnan)(boost::math::jacobi_sn(T(-0.5), T(0.5))));
+#endif
 }