diff --git a/include/boost/math/distributions/non_central_beta.hpp b/include/boost/math/distributions/non_central_beta.hpp
index 00938ab9e4..b78da0521d 100644
--- a/include/boost/math/distributions/non_central_beta.hpp
+++ b/include/boost/math/distributions/non_central_beta.hpp
@@ -257,7 +257,17 @@ namespace boost
             value_type c = a + b + l / 2;
             value_type cross = 1 - (b / c) * (1 + l / (2 * c * c));
             if(l == 0)
-               result = cdf(boost::math::beta_distribution<RealType, Policy>(a, b), x);
+            {
+               if(x < y)
+               {
+                  return invert
+                     ? cdf(complement(boost::math::beta_distribution<RealType, Policy>(a, b), x))
+                     : cdf(boost::math::beta_distribution<RealType, Policy>(a, b), x);
+               }
+               return invert
+                  ? cdf(boost::math::beta_distribution<RealType, Policy>(b, a), y)
+                  : cdf(complement(boost::math::beta_distribution<RealType, Policy>(b, a), y));
+            }
             else if(x > cross)
             {
                // Complement is the smaller of the two:
diff --git a/test/test_nc_f.cpp b/test/test_nc_f.cpp
index 7ad45c1ba3..7ed04ba883 100644
--- a/test/test_nc_f.cpp
+++ b/test/test_nc_f.cpp
@@ -336,6 +336,9 @@ void test_spots(RealType, const char* name = nullptr)
    for (RealType x : x_vals)
    {
       RealType P = cdf(dist_no_centrality, x);
+      RealType Q = cdf(complement(dist_no_centrality, x));
+      // Regression test for #1463: CDF and CCDF must remain complementary for nc=0.
+      BOOST_CHECK_CLOSE(P + Q, RealType(1), tolerance);
       BOOST_CHECK_LE(dist.find_non_centrality(x, a, b, P), tolerance);
    }
    // Case when P=1 or P=0