Comma Splice That!

I have a problem with comma splices. I have always thought that as long as they are relating to the same thought they just need a common in-between them. However, I learned that they have to relate, but needs to have a coordinating conjunction such as; and, so, or, but, and yet. For example, a comma splice would look like this:
I woke up late this morning, I did not have enough time for breakfast.

The correction version would look like this:
I woke up late this morning, so I did not have enough time for breakfast.

Another way you could make this sentence work is if you add a subordinate:
Because I woke up late this morning, I did not have enough time for breakfast.

If you want more information on Comma splices go to
http://www.towson.edu/ows/moduleCS_FS.htm