diff --git a/test/test_bessel_i.hpp b/test/test_bessel_i.hpp
index f6d38f0e0..b2626305c 100644
--- a/test/test_bessel_i.hpp
+++ b/test/test_bessel_i.hpp
@@ -191,7 +191,7 @@ void test_bessel(T, const char* name)
        {
           BOOST_CHECK_EQUAL(boost::math::cyl_bessel_i(T(0.25), T(8000)), std::numeric_limits<T>::infinity());
        }
-       else
+       else BOOST_IF_CONSTEXPR(std::numeric_limits<T>::max_exponent10 < 9200)
        {
           BOOST_CHECK_EQUAL(boost::math::cyl_bessel_i(T(0.25), T(21000)), std::numeric_limits<T>::infinity());
        }
@@ -209,6 +209,8 @@ void test_bessel(T, const char* name)
 #endif
     BOOST_IF_CONSTEXPR (std::numeric_limits<T>::max_exponent > 1000)
     {
+       BOOST_IF_CONSTEXPR(std::is_floating_point<T>::value == false)
+          tolerance *= 2; // multiprecision type.
        BOOST_CHECK_CLOSE_FRACTION(boost::math::cyl_bessel_i(0, T(700)), SC_(1.5295933476718737363162072288904508649662689614661164851272e302), tolerance);
        BOOST_CHECK_CLOSE_FRACTION(boost::math::cyl_bessel_i(1, T(600)), SC_(6.1411813450668919369004006361519512681603654557478168763761e258), tolerance);
     }
diff --git a/test/test_bessel_k.hpp b/test/test_bessel_k.hpp
index 8e59ae225..cf28369c3 100644
--- a/test/test_bessel_k.hpp
+++ b/test/test_bessel_k.hpp
@@ -180,7 +180,7 @@ void test_bessel(T, const char* name)
     BOOST_IF_CONSTEXPR(std::numeric_limits<T>::has_infinity)
     {
        BOOST_CHECK_EQUAL(boost::math::cyl_bessel_k(T(0), T(0)), std::numeric_limits<T>::infinity());
-       BOOST_IF_CONSTEXPR(std::numeric_limits<T>::min_exponent <= -1021)
+       BOOST_IF_CONSTEXPR(std::numeric_limits<T>::min_exponent > -1021)
        {
           BOOST_CHECK_EQUAL(boost::math::cyl_bessel_k(16, ldexp(T(1), -1021)), std::numeric_limits<T>::infinity());
        }
diff --git a/test/test_bessel_y.hpp b/test/test_bessel_y.hpp
index ccbf61f78..8123a777f 100644
--- a/test/test_bessel_y.hpp
+++ b/test/test_bessel_y.hpp
@@ -247,29 +247,42 @@ void test_bessel(T, const char* name)
     BOOST_IF_CONSTEXPR(std::numeric_limits<T>::has_infinity && (std::numeric_limits<T>::min_exponent < -1072))
     {
        static const std::array<std::array<T, 3>, 7> coverage_data = { {
-#if LDBL_MAX_10_EXP > 4931
+#if (LDBL_MAX_10_EXP > 4931) || defined(TEST_MPF_50) || defined(TEST_MPFR_50) || defined(TEST_CPP_DEC_FLOAT) || defined(TEST_FLOAT128) || defined(TEST_CPP_BIN_FLOAT)
           {{ SC_(15.25), ldexp(T(1), -1071), SC_(-9.39553199265929955912687892204143267985847111378392154596e4931)}},
 #else
           {{ SC_(15.25), ldexp(T(1), -1071), -std::numeric_limits<T>::infinity() }},
 #endif
-#if LDBL_MAX_10_EXP > 4945
+#if (LDBL_MAX_10_EXP > 4945) || defined(TEST_MPF_50) || defined(TEST_MPFR_50) || defined(TEST_CPP_DEC_FLOAT) || defined(TEST_FLOAT128) || defined(TEST_CPP_BIN_FLOAT)
           {{ SC_(15.25), ldexp(T(1), -1074), SC_(-5.55960167798850683070863439793e+4945)}},
 #else
           {{ SC_(15.25), ldexp(T(1), -1074), -std::numeric_limits<T>::infinity() }},
 #endif
-#if LDBL_MAX_10_EXP > 9872
+#if (LDBL_MAX_10_EXP > 9872) || defined(TEST_MPF_50) || defined(TEST_MPFR_50) || defined(TEST_CPP_DEC_FLOAT) || defined(TEST_FLOAT128) || defined(TEST_CPP_BIN_FLOAT)
           {{ SC_(31.25), ldexp(T(1), -1045), SC_(-1.64443614527479263825137492596041426343778386094212520006e9872)}},
 #else
           {{ SC_(31.25), ldexp(T(1), -1045), -std::numeric_limits<T>::infinity() }},
 #endif
+#if defined(TEST_MPF_50) || defined(TEST_MPFR_50) || defined(TEST_CPP_DEC_FLOAT) || defined(TEST_FLOAT128) || defined(TEST_CPP_BIN_FLOAT)
+          // Our exponent range may be so extreme that we can't trigger the coverage cases below, so use a copy of previous cases here
+          // as a placeholder.
+          {{ SC_(15.25), ldexp(T(1), -1071), SC_(-9.39553199265929955912687892204143267985847111378392154596e4931)}},
+          {{ SC_(15.25), ldexp(T(1), -1071), SC_(-9.39553199265929955912687892204143267985847111378392154596e4931)}},
+#else
           {{ SC_(233.0), ldexp(T(1), -63), -std::numeric_limits<T>::infinity() }},
           {{ SC_(233.0), ldexp(T(1), -64), -std::numeric_limits<T>::infinity() }},
-#if LDBL_MAX_10_EXP > 413
+#endif
+#if (LDBL_MAX_10_EXP > 413) || defined(TEST_MPF_50) || defined(TEST_MPFR_50) || defined(TEST_CPP_DEC_FLOAT) || defined(TEST_FLOAT128) || defined(TEST_CPP_BIN_FLOAT)
           {{ SC_(200.25), SC_(1.25), SC_(-3.545198572052800784992190965856441074217589237581037286156e413)}},
 #else
           {{ SC_(200.25), SC_(1.25), -std::numeric_limits<T>::infinity()}},
 #endif
+#if defined(TEST_MPF_50) || defined(TEST_MPFR_50) || defined(TEST_CPP_DEC_FLOAT) || defined(TEST_FLOAT128) || defined(TEST_CPP_BIN_FLOAT)
+          // Our exponent range may be so extreme that we can't trigger the coverage cases below, so use a copy of previous cases here
+          // as a placeholder.
+          {{ SC_(15.25), ldexp(T(1), -1071), SC_(-9.39553199265929955912687892204143267985847111378392154596e4931)}},
+#else
           {{ SC_(1652.25), SC_(1.25), -std::numeric_limits<T>::infinity()}},
+#endif
       } };
 
        do_test_cyl_neumann_y<T>(coverage_data, name, "Extra Coverage Data");
diff --git a/test/test_binomial_coeff.hpp b/test/test_binomial_coeff.hpp
index 0c6762c6f..a790a2c53 100644
--- a/test/test_binomial_coeff.hpp
+++ b/test/test_binomial_coeff.hpp
@@ -83,9 +83,11 @@ void test_binomial(T, const char* type_name)
    //
    BOOST_CHECK_THROW(boost::math::binomial_coefficient<T>(2, 3), std::domain_error);
    T tolerance = boost::math::tools::epsilon<T>() * 200;
-#if LDBL_MAX_10_EXP > 320
+#if (LDBL_MAX_10_EXP > 320) || defined(TEST_MPF_50) || defined(TEST_MPFR_50) || defined(TEST_CPP_DEC_FLOAT) || defined(TEST_FLOAT128) || defined(TEST_CPP_BIN_FLOAT)
    BOOST_IF_CONSTEXPR(std::numeric_limits<T>::max_exponent10 > 320)
    {
+      BOOST_IF_CONSTEXPR(std::is_floating_point<T>::value == false)
+         tolerance *= 2;
       BOOST_CHECK_CLOSE_FRACTION(boost::math::binomial_coefficient<T>(1072, 522), SC_(8.5549524921358966076960008392254468438388716743112653656397e320), tolerance);
    }
    else BOOST_IF_CONSTEXPR(std::numeric_limits<T>::has_infinity)
@@ -98,12 +100,13 @@ void test_binomial(T, const char* type_name)
       BOOST_CHECK_EQUAL(boost::math::binomial_coefficient<T>(1072, 522), std::numeric_limits<T>::infinity());
    }
 #endif
-#if LDBL_MAX_10_EXP > 4946
+#if (LDBL_MAX_10_EXP > 4946) || defined(TEST_MPF_50) || defined(TEST_MPFR_50) || defined(TEST_CPP_DEC_FLOAT) || defined(TEST_FLOAT128) || defined(TEST_CPP_BIN_FLOAT)
+
    BOOST_IF_CONSTEXPR(std::numeric_limits<T>::max_exponent10 > 4946)
    {
       BOOST_CHECK_CLOSE_FRACTION(boost::math::binomial_coefficient<T>(16441, 8151), SC_(5.928641856224322477306131563286843903129818155323061805272e4946), tolerance);
    }
-   else BOOST_IF_CONSTEXPR(std::numeric_limits<T>::has_infinity)
+   else BOOST_IF_CONSTEXPR(std::numeric_limits<T>::has_infinity && (std::numeric_limits<T>::max_exponent10 < 4950))
    {
       BOOST_CHECK_EQUAL(boost::math::binomial_coefficient<T>(16441, 8151), std::numeric_limits<T>::infinity());
    }