Most specific match using between

Hi people, is there a swtich or something to instruct a between statement
hat it must perform a most specific match ?
These are the details, i have these table

name | start | end
---------------+---------------+-----------------
general | 2660000 | 2669999
specific | 2660124 | 2660124
(2 rows)

unsing the query: select name where '2660124' between start and end

i got:

name
---------
general
specific

How can i get only specific?

thanks