Signal Phasing where one way grid ends, and st. becomes two-way.

[Brian556]

]http://maps.google.com/maps?hl=en&ll=33.214518,-97.132477&spn=0.000004,0.003133&t=m&z=19&layer=c&cbll=33.214527,-97.132692&panoid=kkoCcaIgrOAnJBjcihlmTg&cbp=12,69.23,,0,0]

The intersection of Locust and Hickory on Denton Texas has this situation, and the signal phasing is very non-functional and unsafe in my opinion.
Traffic turning left from Hickory to Locust goes at the same time as traffic turning right from WB Hickory to Locust (an "ALL TRAFFIC MUST TURN RIGHT situation). The problem with this is that the traffic turning left sees no oncoming traffic to yield to, because the oncomong traffic is to the right of them(because of hte wide throat of the intersection), whereas, of course it is conventionally on the left. Notice the two pickups in the Streetviw image. If their timing were slightly different, they might have collided. As far as I know, this is legal, but unsafe bacuse it sends opposing directions into the same space at the same time. I think split phasing should be required here, and anywhere oncoming traffic that you are supposed to yield to is not to the left of you.

Another issue here is that there is no advanced warning of two way traffic beyond the intersection. The two way trafic sign in the Streetview image at he intersection has since disappeared.

[Alps]

Split phasing should definitely be used when the roads are offset to each others' right, for the reason you mention.