I'm assuming 900 USD for the budget then so if you're happy with something bigger and heavier, this would be good:
PCPartPicker part list:
http://pcpartpicker.com/p/GLmmZL
Price breakdown by merchant: http://pcpartpicker.com/p/GLmmZL/by_merchant/
CPU: Intel Core i5-4460 3.2GHz Quad-Core Processor ($166.95 @ SuperBiiz)
CPU Cooler: Noctua NH-L9x65 33.8 CFM CPU Cooler ($59.99 @ Amazon)
Motherboard: ASRock H97M-ITX/AC Mini ITX LGA1150 Motherboard ($72.98 @ Newegg)
Memory: G.Skill Ripjaws X Series 8GB (2 x 4GB) DDR3-1600 Memory ($48.99 @ Newegg)
Storage: Samsung 850 EVO-Series 500GB 2.5" Solid State Drive ($161.99 @ Amazon)
Video Card: Gigabyte GeForce GTX 750 Ti 2GB WINDFORCE Video Card ($109.99 @ Newegg)
Case: Silverstone RVZ01B Mini ITX Desktop Case ($79.99 @ Directron)
Power Supply: Silverstone 450W 80+ Bronze Certified SFX Power Supply ($59.99 @ NCIX US)
Total: $760.87
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-07-05 16:31 EDT-0400
You could even go for a more powerful GPU but you might struggle for cooling in such a small case.
Anything smaller is either going to involve a half height graphics card or the integrated graphics on an AMD A10, neither of which are likely to be nearly as powerful as the GPU in the Alienware.