Lordsburg, NM to Deming, NM

[MLB]

I'm planning a trip between Phoenix and las Cruces.  The only leg I have questions about is Lordsburg to Deming, NM.  Does anyone know a route that does not go through Silver City?  There is a frontage road all but about 11 miles from Deming to Las Cruces.  The NM highway patrol says get on I-10 at mile marke 116 and off at 127, frontage road the rest of the way.  The NMHP does not have any problem with bicycles on the freeway shoulder but i want to avoid it as much as possible.  No problems in Arizona, just along I-10.

[aggie]

Unfortunately there isn't much between Lordsburg and Deming.  If you want to stay on paved roads you are limited to the I10 or its frontage road.