How to get new kitty to sleep through the night?

Hey guys! Its been awhile since I've posted here. I've just adopted a new kitty about 2 weeks ago named Jesse. He's a total sweetheart. A little bit of a scardey cat but finally starting to get used to me and his new environment. Here he is!
 


However I'm having bit of trouble with his sleeping habits. My previous cat, who passed away in March, pretty much always slept through the night so I'm used to that. I would play with him before bed, feed him, and he'd be out until 530AM or so. With Jesse, however, even though I play with him before bed and feed him, he consistently wakes up at 3AM and runs around meowing (sometimes plays with a toy) and then he'll wake up a couple hours later at 5AM and do the same thing all over. I don't mind the 5AM so much...its more-so when he gets up earlier than that.

I've been trying to play with him even more in the evenings, sometimes up to 3 different times throughout the evening. He's not super playful but he does engage with the toys and runs after them quite a bit, so he is getting some exercise. I'll feed him canned food around 10PM after the last play session. I'm just not sure what to do at this point. I live in a studio so if he's running around, I hear him, and unfortunately since I have sweaky floors, my neighbor below me probably does too which I feel bad about. I just haven't been able to get a full night's sleep in the past 2 weeks.

Is there anything else you'd suggest? As far as health is concerned, he has dental issues which are getting treated in June (teeth cleaning and extraction). He also was reported as having a level 2 heart murmur by the shelter, but my own vet did not detect anything last week after listening for awhile. I've noticed also he's scratching quite a bit, especially right after getting out of bed...fleas possibly? I think he's due for his flea medication in about a week.

Thanks!

I'm sorry about the loss of your first kitty.  It's tough getting used to a new one's energy!  

I found this link about 'night crazies' http://www.thecatsite.com/a/cats-and-night-crazies  but now re-reading your post, it sounds like you're already playing with him and giving him a snack afterwards.  

How old is Jesse?  

I'm sorry about the loss of your cat. 

I had had this problem with Minnie. She would lay down and nap for a while, but would get pretty active around 2AM or so, playing and meowing. She likes to lay under blankets, for whatever reason, and I started covering her with one at night. Once I started doing that, she started sleeping through the night (occasionally getting up to use the litter box or drink water). Maybe that would help you? I know it's weird advice!

Thanks, guys! He's 3 years old I've recently found a toy that he really likes, and I've been using that before bed. It gets him running around a ton and I think that's helping slightly. He still gets up, but he doesn't seem to be bursting with energy as much. That's interesting about the blankets! Unfortunately its just too hot here for that right now but I may try that as the weather gets colder.