>>You may also try

 ... WHEN @FirstOfTheMonth + 0 BETWEEN StartDate And EndDate
>>-- instead of
>> ... WHEN StartDate <= @FirstOfTheMonth + 0 And EndDate >= @FirstOfTheMonth + 0
>>

I'm not sure if SQL Server could use any index to optimize query in this case.
>=========
>Why do you have only 29 days and why you have slightly different condition for the last day?
>
>I agree about using between... Funny, we're usually have something like
>field between FixedDay1 and FixedDay2, so it's hard to understand in the other way around, though should work as well.
>

You missed '...' after day29. :) I didn't want to repeat 30&31 because they are similar to 29. Not every month have 29 or more days. That's why there's additional check for that starting with day29.