Just like the mullen mouth snaffle, a curb with a straight mouthpiece is also referred to as a mullen mouth. While most curbs have some degree of port (an elevated curve in the middle of the mouthpiece), the mullen mouth has no port, but often a slightly bowed shape from cheek to cheek. A mullen mouth curb is also often found with a rubberized mouthpiece.
The advantage of the mullen mouth is that it affords very even pressure over the tongue, and there is no danger of the port pressing upwards on the palate. On the other hand, because the lack of a port does not give the tongue the ability to move up, more pressure is placed over the tongue than on the bars, making it possibly a more restrictive bit for the tongue.