Looking for a GPU that will fit

[CIblue]

Needing to upgrade my GPU, but only have space for a 7" x 1.5" x 5" size card at max. I originally wanted a GTX 760 or R9 270X, but those are too big. Does anyone know of a similar card that would fit. I have looked at the GTX 750Ti, but I've heard it requires a certain type of 300W PSU. PSU isn't as much an issue, cause I'm going to have to buy a new one anyways (pretty certain my 180W won't work with anything that I'm wanting).

Current System Specs:
Lenovo H410 7724
Processor: Pentium Dual Core E5800 3.2 GHz
Mainboard: Lenovo 7724-1AU
HDD: 500GB
Memory: 2 x 2048 MB DDR3
GPU: AMD Radeon HD 5450
PSU: AcBel PC8061 180W

This is basically the same thing I have, apart from the GPU (which I upgraded to the HD 5450 about 3 years ago): http://www.tigerdirect.com/applications/SearchTools/item-details.asp?EdpNo=1165207
This is the PSU that I have: http://www.amazon.com/Lenovo-ThinkCentre-TFX12V-54Y8835-PC8061/dp/B00PRB7AOQ

 

[Sakata]

Firstly what exactly is your budget? Also why not buy a new case, with rebates and good shopping skills and a bit of luck you can pick something really good up sub $50, like a Corsair case then maybe get their CX430 which often goes on sale with rebate for $20.

Edit : although honestly it might be a good idea to save up for a whole new PC, good shopping and rebates and such means a nice one can be had for sub $600. ( and a lot of people have said that but I have really put it into practice and it works.)

 

[CIblue]

Firstly what exactly is your budget? Also why not buy a new case, with rebates and good shopping skills and a bit of luck you can pick something really good up sub $50, like a Corsair case then maybe get their CX430 which often goes on sale with rebate for $20.

Edit : although honestly it might be a good idea to save up for a whole new PC, good shopping and rebates and such means a nice one can be had for sub $600. ( and a lot of people have said that but I have really put it into practice and it works.)

The case is big enough for a 9" (maybe more), it's the motherboard that is the problem. 7" puts the edge of the GPU 1mm from one of my 2GB Mem cards.

 

[Sakata]

Then I would look a dimensions of cards like the 750ti and pick up a Corsair CX400 power supply. Should cost between $80 and $150 depending on versions, sales, taxes, shipping, etc.