Unfortunately it is true that pets can limit your rental choices. Some owners will not take either a dog or a cat based on a past bad experience with either animal. Sometimes the owner can not take any pets based on allergies. This can be an arbitrarily made decision by the owner and as a renter it can be painful to be barred from a property based on your furry friend. Try to seek out at pet loving broker that will have knowledge of the best cat friendly places.
Based on my experience in the New York city market it is always best to offer up full disclosure on your pets. Many rental clients that have pets put together a packet to present to the landlord. The packet can include a picture, bio, and additional details that present why your pet will not negatively impact the property. Examples of this would be certain breed benefits such as if your cat is a hypoallergenic breed like a Balinese, or if it were a dog perhaps it is a highly trained service dog or a docile breed. Also important is to detail your care of the animal so in the case of dogs you might want to include that the dog is out at doggie daycare on weekdays or with a dog-walker a certain number of days during the week.
Your cat is older so that is an example of a benefit that you would want to present (hopefully the landlord will perceive that your cat is not as frisky and mischievous as a kitten might be). Best of luck to you and remember to never try to downplay or hide the fact that you have a pet. I have seen terrible examples of pet disputes (http://therealdeal.com/blog/2013/07/22/husband-of-town-broke ) and it is never worth the hassle! Live in peace with a landlord that accepts or better yet likes your cat.
I would use a local rental professional to save time and money and also to make sure you don't miss a great rental.
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I have several different approaches..never just one standard strategy...as landlords/properties/and situations always differ. Also I have had Dozens of experiences where owners blurted out "no" when their agents or family members just quickly asked them if the prospective tenant could bring their pet. Of course the landlord is probably going to say no in that setting & case. They didn't speak to seasoned, polished professional..who is prepared with what & how to say it.. so he forms a different image than the one blurted out by an agent (on his side of the transaction) that probably doesn't care if its a yes or no outcome. I have had many that where "loosened up" and gently nudged to being more open-minded. One of the Biggest differences I have observed is the person attempting the negotiation needs to Almost Always be Very experienced and talented at their tact and strategy moving this forward. If this is not the case...the percentage of "No's" you get skyrockets instantly. "No" is very often not always a definitive..Ultimatum "NO".. I have seen it become "Ok" Many times. Of course.. not Always though...& there may be a string of No's you hit without having some success. Unless you have no time (or have no resilience)..don't give up so easily.
!!!-Work with someone that is Very good at negotiating AND has done this Not once but Multiple times before-!!! Pay them a fee for their skill & successful talents & move forward with it. A fee is just ONE time only.. and a tenant gets to enjoy month after month, year after year.. the success that the skilled pro negotiated on their behalf. Always be willing to think outside the narrow Boundries!