If you have not looked at the list of databases available at FamilySearch lately, it may well be worth you time to do so. Recently, FamilySearch has added an impressive number of databases that provide images you can browse through. Those collections have not been indexed yet, but that should not stop you form exploring them if they included the type of record and time frame you are interested in.
One way to reveal those record sets is to scroll down the FamilySearch home page (yes, go right by that tempting search form you initially see on the page), until you come to a list of locations. Click on your location of interst, "United States" for example, and you will be shown an alphabetized list of available record sets. You can scroll down the list, or click on a state listed in the left panel of the screen. Since the list of record sets is getting so large, clicking on the state can be a real time-saver.
Notice in the column to the right of the record collection title you will see one of two entries: one will be the number of records in the collection, and the other will be the words "Browse Images." Those are the collections that are not yet indexed. It's a bit more work to look through those records (takes us back to those delightful hours spent in front of microfilm readers), but you will see records that will not turn up if you do your usual name search.