How to make my ELF run with both new and old version of glibc?

When I'm compiling my elf, it is "best practice" to make it link against the oldest version of glibc I can, so it will work both on new and old versions of glibc. i.e. if I use realpath, which in readelf output of glibc we can see has both a GLIBC_2.0 version and a GLIBC_2.3 version, I want to use the old version so my ELF would work on glibc 2.0/1/2. But the GLIBC_2.3 version was probably developed and upgraded since it was published, and I guess GLIBC_2.0 version hasn't changed since glibc 2.3 has been published. So I guess I want my elf to use GLIBC_2.3 version when it is present, and when not, to fallback to the GLIBC_2.0 version. Is is possible? Or what don't I understand?