Hi Lauri,
You have been of enormous help. the URL you suggest as a resource is an excellent beginning as it can be used to search a surname. The next step is to search through all of the many records available. See:
http://www.ra.ee/dgs/explorer.php?tid=3&tbn=1&lev=yes&hash=73ef5859c6eb58960b3940775df6102f
Enormously time consuming but potentially invaluable particularly if you know the name of the county, for example, Parnu and the name of the parish in that county, e.g., Lutheran, St, Elizabeths, and so on. I have just started to search these records. No success thus far.
But as I know the exact date of my grand-uncle Michael Martinson's birth in Parnu, 25 Dec 1886, I have hope!
Thanks again,
David