When you transfer to secondary you need to have as little airspace above the beer as possible.....because you do not want oxygen in contact with beer or it can make trhe beer skunky from oxidation....this is not a problem in primary because during active fermentation the yeast creates plenty of CO2 to push the oxygen out and protects the surface of the beer (fills the airspace above in the bucket). So for secondary....if you did a 5 gallon batch of beer....you need to use a 5 gallon carboy.
Now with that being said.....a lot of experienced brewers on this site do not even do secondary (including me) as it is not necessary in most cases.....some exceptions would be for certain types of beers or for fruit additions, lagering, etc. But in general you are better off not going to secondary as you just risk contamination (infection) during the transfer. I normally keep my beers in primary 3 weeks....then bottle (as long as fermentation is done after a FG check).
What type of beer are you talking about?