Later models of the J-79 had - supposedly - smokeless combustors fitted, although the smoketrail was still evident.
Late in the F-4G's service life 'Pacer Frugal' - IIRC - modifications were also fitted in an attempt to improve reliability and further reduce the smoke but it never disappeared altogether, even RAF/RN's F-4M/K were good smokers when not using re-heat.
Regards, RP.