Question first: What are some feasible alternatives to time tracking for employees in a web/software development company, and why are they better options

Explanation:

I work at a company where we work like this. Everybody is paid salary. We have 3 types of work, Contract, Adhoc and Internal (Non billable). Adhoc is just small changes that take a few hours and we just bill the client at the end of the month. Contracts are signed and we have this big long process, the usual.

We figure out how much to charge by getting an estimation of the time involved (From the design and the developers), multiplying it by our hourly rate and that's it. So say we estimate 50 hours for a website. We have time tracking software and have to record the time in 15 we spend on it (7:00 to 7:15 for example), the project name, and give it some comments.

Now if we go over the 50 hours, we are both losing money and are inefficient.

Now that I've explained how the system works, my question is how else can it be done if a better method exists (Which I'm sure one must). Nobody here likes the current system, we just can't find an alternative. I'd be more than willing to work after hours longer hours on a project to get it done in time, but I'm much inclined to do so with the current system. I'd love to be able to sum up (Or link) to this post for my manager to show them why we should use abc system instead of this system.