Rhodium (Rh) is found similar to Palladium (Pd) in making near-Ohmic electrical contacts to single-walled carbon nanotubes (SWNTs) with diameters d>similar to 1.6 nm. Non-negligible positive Schottky barriers (SBs) exist between Rh or Pd and semiconducting SWNTs (S-SWNTs) with d <similar to 1.6 nm. With Rh and Pd contacts, the characteristics of SWNT field-effect transistors and SB heights at the contacts are largely predictable based on the SWNT diameters, without random variations among devices. Surprisingly, electrical contacts to metallic SWNTs (M-SWNTs) also appear to be diameter dependent especially for small SWNTs. Ohmic contacts are difficult for M-SWNTs with diameters <=similar to 1.0 nm possibly due to tunnel barriers resulted from large perturbation of contacting metal to very small diameter SWNTs due to high chemical reactivity of the latter. (C) 2005 American Institute of Physics.