//exclude the -0.10f to 0.10f range
float xRot = entity.Rotation.X;
if (xRot < 0f && xRot > -0.10f) xRot = -0.10f;
else if (xRot > 0f && xRot < 0.10f) xRot = 0.10f;

//use the new X value in the rotation vector3
Vector3 rot = new Vector3(xRot, entity.Rotation.Y, entity.Heading - 20f);