After owning my Lotus 10 years I finally decided to upgrade the sound system. I'm gonna build something really close to whats on my Jeep which shares terrible acoustics like the Lotus and even has similar sized speakers.
Having built many systems in the past, no matter how good of a speaker you buy you will not get good sound unless the speakers are amp'd. Underdriven speakers will distort when you turn up the volume so in my opinion its pointless to spend money on a good speaker without having the power to run them.
As Exigegus stated, another key is not to ask a little speaker to put out lower frequencies, even amped, they have a hard time playing such a wide range, so adding a little sub is a good idea. I have an amped 8" sub on my Jeep and its more than enough bass (for me) and lets the 4 little speakers play the higher frequencies.
I would recommend getting this little amp that should fit next to the headunit, I havent gotten mine yet but highly confident it will fit in back of the dash after I took a look back there, and the wiring is really easy as you don't need to bother with RCAs or power to the battery if you dont want to.
Alpine KTP-445U (or the 445A if using an Alpine deck).
Alternately, if you don't mind running cables and want more power, the Rockford Fosgate PBR300x4 is what I run in my Jeep but I doubt this one will fit in back of the dash even though its only a little bigger than a pack of cigarettes but it will definitely fit in back of the seat or many other places.
Depending on your budget I would start with the Alpine amp at just a little over $100 and pair it with your current speakers and if your still desire a little more add a sub and some new speakers like Polk, JL, or Focal speakers and even a better headunit.