diff --git a/include/boost/math/tools/precision.hpp b/include/boost/math/tools/precision.hpp
index 94c22b55ed..6e863401d9 100644
--- a/include/boost/math/tools/precision.hpp
+++ b/include/boost/math/tools/precision.hpp
@@ -182,9 +182,13 @@ struct log_limit_traits
 {
    typedef typename boost::math::conditional<
       (boost::math::numeric_limits<T>::radix == 2) &&
-      (boost::math::numeric_limits<T>::max_exponent == 128
-         || boost::math::numeric_limits<T>::max_exponent == 1024
-         || boost::math::numeric_limits<T>::max_exponent == 16384),
+      (
+         (     boost::math::numeric_limits<T>::max_exponent == 128
+            || boost::math::numeric_limits<T>::max_exponent == 1024
+            || boost::math::numeric_limits<T>::max_exponent == 16384
+         )
+         && (-boost::math::numeric_limits<T>::min_exponent10 + 1 == boost::math::numeric_limits<T>::max_exponent10)
+      ),
       boost::math::integral_constant<int, (boost::math::numeric_limits<T>::max_exponent > (boost::math::numeric_limits<int>::max)() ? (boost::math::numeric_limits<int>::max)() : static_cast<int>(boost::math::numeric_limits<T>::max_exponent))>,
       boost::math::integral_constant<int, 0>
    >::type tag_type;
diff --git a/reporting/performance/test_kn.cpp b/reporting/performance/test_kn.cpp
index bf2c8cda19..2f309f625e 100644
--- a/reporting/performance/test_kn.cpp
+++ b/reporting/performance/test_kn.cpp
@@ -48,7 +48,7 @@ static const std::array<std::array<T, 3>, 9> kn_data = { {
    { { SC_(-10.0), SC_(1.0), SC_(1.80713289901029454691597861302340015908245782948536080022119e8) } },
    { { SC_(100.0), SC_(5.0), SC_(7.03986019306167654653386616796116726248616158936088056952477e115) } },
    { { SC_(100.0), SC_(80.0), SC_(8.39287107246490782848985384895907681748152272748337807033319e-12) } },
-   { { SC_(-1000.0), SC_(700.0), SC_(6.51561979144735818903553852606383312984409361984128221539405e-31) } },
+   { { SC_(-129.0), SC_(200.0), SC_(3.61744436315860678558682169223740584132967454950379795115566e-71) } },
    } };
 
 int main()
diff --git a/test/test_bessel_k.hpp b/test/test_bessel_k.hpp
index 6a2a8179d9..36b86bec5e 100644
--- a/test/test_bessel_k.hpp
+++ b/test/test_bessel_k.hpp
@@ -133,7 +133,7 @@ void test_bessel(T, const char* name)
         {{ SC_(-10.0), SC_(1.0), SC_(1.80713289901029454691597861302340015908245782948536080022119e8) }},
         {{ SC_(100.0), SC_(5.0), SC_(7.03986019306167654653386616796116726248616158936088056952477e115) }},
         {{ SC_(100.0), SC_(80.0), SC_(8.39287107246490782848985384895907681748152272748337807033319e-12) }},
-        {{ SC_(-1000.0), SC_(700.0), SC_(6.51561979144735818903553852606383312984409361984128221539405e-31) }},
+        {{ SC_(-129.0), SC_(200.0), SC_(3.61744436315860678558682169223740584132967454950379795115566e-71) }},
     }};
     static const std::array<std::array<typename table_type<T>::type, 3>, 11> kv_data = {{
         {{ SC_(0.5), SC_(0.875), SC_(0.558532231646608646115729767013630967055657943463362504577189) }},
diff --git a/test/test_bessel_k_prime.hpp b/test/test_bessel_k_prime.hpp
index f43728c118..79df46c703 100644
--- a/test/test_bessel_k_prime.hpp
+++ b/test/test_bessel_k_prime.hpp
@@ -131,7 +131,7 @@ void test_bessel(T, const char* name)
         {{ SC_(-10.0), SC_(1.0), SC_(-1.8171379399979651461891429013401068319174853467388121e9) }},
         {{ SC_(100.0), SC_(5.0), SC_(-1.4097486373570936520327835736048715219413065916411893e117) }},
         {{ SC_(100.0), SC_(80.0), SC_(-1.34557011017664184003144916855685180771861680634827508e-11) }},
-        {{ SC_(-1000.0), SC_(700.0), SC_(-1.136342773238774160870536985092768591616106526374957e-30) }},
+        {{ SC_(-129.0), SC_(200.0), SC_(-4.3110345255133348027545113739271337415489367194240537230455182e-71) }},
     }};
     static const std::array<std::array<T, 3>, 11> kv_prime_data = {{
         {{ SC_(0.5), SC_(0.875), SC_(-0.8776935068732421581818610624499915196588910540138553643355820) }},