diff --git a/numpyro/distributions/directional.py b/numpyro/distributions/directional.py
index 8156855b1..e3e5dd3ee 100644
--- a/numpyro/distributions/directional.py
+++ b/numpyro/distributions/directional.py
@@ -8,6 +8,7 @@
 import operator
 
 from jax import lax
+from jax.lax import stop_gradient
 import jax.numpy as jnp
 import jax.random as random
 from jax.scipy import special
@@ -311,7 +312,9 @@ class SineBivariateVonMises(Distribution):
             \frac{\rho}{\kappa_1\kappa_2} \rightarrow 1
 
         because the distribution becomes increasingly bimodal. To avoid bimodality use the `weighted_correlation`
-        parameter with a skew away from one (e.g., Beta(1,3)). The `weighted_correlation` should be in [0,1].
+        parameter with a skew away from one (e.g.,
+        `TransformedDistribution(Beta(3,3), AffineTransform(loc=-1, scale=2))`).  The `weighted_correlation`
+        should be in [-1,1].
 
     .. note:: The correlation and weighted_correlation params are mutually exclusive.
 
@@ -404,7 +407,10 @@ def norm_const(self):
             jnp.log(jnp.clip(corr**2, jnp.finfo(jnp.result_type(float)).tiny))
             - jnp.log(4 * jnp.prod(conc, axis=-1))
         )
-        fs += log_I1(49, conc, terms=51).sum(-1)
+        num_I1terms = jnp.maximum(
+            501, jnp.max(self.phi_concentration) + jnp.max(self.psi_concentration)
+        ).astype(int)
+        fs += log_I1(49, conc, terms=stop_gradient(num_I1terms)).sum(-1)
         norm_const = 2 * jnp.log(jnp.array(2 * pi)) + logsumexp(fs, 0)
         return norm_const.reshape(jnp.shape(self.phi_loc))
 
diff --git a/test/test_distributions.py b/test/test_distributions.py
index 20da4165d..1e2b3be05 100644
--- a/test/test_distributions.py
+++ b/test/test_distributions.py
@@ -3464,3 +3464,16 @@ def test_gaussian_random_walk_linear_recursive_equivalence():
     x2 = dist2.sample(random.PRNGKey(7))
     assert jnp.allclose(x1, x2.squeeze())
     assert jnp.allclose(dist1.log_prob(x1), dist2.log_prob(x2))
+
+
+@pytest.mark.parametrize("conc", [1.0, 10.0, 1000.0])
+def test_sine_bivariate_von_mises_norm(conc):
+    dist = SineBivariateVonMises(0, 0, conc, conc, 0.0)
+    num_samples = 500
+    x = jnp.linspace(-jnp.pi, jnp.pi, num_samples)
+    y = jnp.linspace(-jnp.pi, jnp.pi, num_samples)
+    mesh = jnp.stack(jnp.meshgrid(x, y), axis=-1)
+    integral_torus = (
+        jnp.exp(dist.log_prob(mesh)) * (2 * jnp.pi) ** 2 / num_samples**2
+    ).sum()
+    assert jnp.allclose(integral_torus, 1.0, rtol=1e-2)