I book as much as I can through BA travel shops - I now this is no use to you in the US - but that way I get miles on my spend and they are part of BA, so there is only one person to blame/sort things out if they go wrong.

Until recently I had to have everything booked through the Corporate Travel department, but as they report to me I made an exception for myself with some silly excuse about lack of audit control if a department that reports me books my flights!

If you need to book flights/hotels/cars in the UK I very strongly recommend the BA travel shops, they have a great knowledge of the requirements of business travellers and will happily offer a non-BA flight if it is more suitable.