There are three main casuses of non-chlamydial non-gonococcal urethritis. These are Ureaplasma,
Mycoplasma, and Trichomonas. They are not tested
for with the typical battery of STD tests in the US, though they are in some other countries.
Tests are available through LabCorp, they are often not covered by insurance.
Mycoplasma/Ureaplasma, Real-Time PCR
http://www.labcorp.com/datasets/labcorp/html/chapter/mono/vm003300.