3 speaker car audio system

Hello, I have a classic car and I like to have a car stereo but I don't want to ruin the car by cutting big holes in parcel shelf or door cards.   The car has space for some very small 13cm speakers in the doors with proper grills provided by the manufacturer. 

Obvously those tiny speakers will only do well with mid-range and trebble.  I'd like to add a bit of bass to the system.  I don't want to spend a lot of money and I'm not a bass junkie. I just want a stereo good for playing the crap pop music I like to listen to. I don't really want to buy a new amp, I'd rather use the one inside the stereo.  So I want a really small bass speaker and I guess I can use an external cross-over unit to split the signal from the stereo to the different speakers.

I'd like some recommendations for good ways to try to achieve what I'm after.  I can't use a lot of space either.  Probably a 6-inch sub if possible.

Erm, guess you mean something in a box in the boot?  I don't want anything like that.  Have you got any links or pictures to the sort of thing you were thinking of?

Even though bass is non-directional so shouldn't matter if the bass speaker is in the boot, I still think that isn't what I'm looking for.  I want a small bass speaker in the front of the car.  There is a space for a large single speaker in the original centre console.  I'd like to put it there, or hide it under the dash behind the centre console. 

This idea is meant as a cheat to get a balanced sound from a system using a small number of small speakers to avoid minimal / invisible modification to the original interior of the car.  Think about those small speaker systems made to work with computers which still produce a reasonable sound even though they're tiny.  I'm looking to replicate that sort of setup in a car. 

If I could, I would just cut some big holes in the parcel shelf and wack in a set of 6x9's instead.  But like I say, trying to do it without cutting up the car.

You could use something like the Aura bass shaker, or butt kicker.  Believe they are basically a servo driver.  Just a motor, they don't have all the parts of a speaker, and don't require an enclosure.  I've not used either in a car. I  have experience with the larger servo drivers in a pro audio set up, but they are a little different.  Huge motors and they do use an enclosure. 

I believe the butt kicker or bass shaker are gonna give the feel of bass than the sound.   Either way having sub bass and just basically tweeters is not gonna yield very good sound.  Might look into custom kick panels or something to get some full range speakers in that thing.  You could use these without nearly any modification to the vehicle, and they would be much better for sound quality.