Caldonians were committed to pure research and built their reputation around that dedication. They were wary of things which distracted from their research, such as administrative demands.
In 2366, the Caldonians were one of several species that negotiated for rights to the Barzan wormhole. Leyor was sent as their representative to talks held aboard the USS Enterprise-D. They were bought out by Devinoni Ral, who represented the Chrysalians. Ral brought up the tremendous amount of administration that would be needed to manage the wormhole and the high amount of traffic it would experience, which the Caldonians felt they were unable to handle. Commander William T. Riker, representing the Federation in Doctor Mendoza's absence, wanted to acquire their bid of trillium 323, but the substance had been purchased by Ral before the Caldonians announced their withdrawal. Ral used the material to his advantage during the continuing negotiations between the Chrysalians, the Ferengi, and the Federation. (TNG: "The Price")
According to an internal reference document, listing all the aliens seen in Star Trek: The Next Generation, which was circulated around the time of the production of TNG Season 5, the Caldonians were given the description of "A race of three fingered beings over six feet tall, enlarged craniums include a raised bony framework shaped like a perpendicular theta."
According to Michael Westmore, "The Caldonians were my first attempt to do something really elaborate with an alien forehead, as opposed to some of the simple humanoids we had been doing up to that point. [...] Kevin was our big makeup. I spent a lot of time designing a large, extended forehead for him, which further emphasized his height, and we worked closely with the wardrobe department, who created a headdress that reduced the amount of rubber we had to use. Wardrobe also made a set of three-fingered gloves which changed the shape of Peter's hands. The overall design worked very well, and it set the stage for some of the more complicated work we'd be doing in the future." (Star Trek: The Next Generation Makeup FX Journal, p. 74-75)