HELP!! Question about Changing Terms in your Rental Advertisement

[Stephen G.]

I have a general question about advertising a rental (in Upstate New York) - If I post an apartment listing with certain criteria or stipulations (eg. rent price, pets/no pets, smoking/non-smoking) only to find out that either my rent is too high or I'm leaving out a huge market share of tenants because of a "no pets policy", how can I go about changing my listing criteria without it being considered "discriminatory" against the applicants I have already turned down based on my previous stipulations? Is it even possible to change my criteria this time around?? Thanks in advance for your help!