Not long ago I installed Thudbusters on my wife's Yeah <Helios> and my Raleigh 20. After settling for the right elastomers, we were very impressed by the ability for bumps and shock to be smoothed over.
It really make a massive difference in some cases, eg on my wife's favourite ride, the Warburton rail trail, there is a very long bridge with rough transverse slats (did I say rough?) which makes for a very harsh jarring bumpy ride. On a narrow tyred bike you typically have to get off and walk. Not so with the Thudbusters. I ceases to be an issue. What also works well is pedalling with high cadence - there is not much of an issue with bouncing in the saddle.
Then I got the Downtube Mini with built-in rear suspension. I thought that because there is less sprung mass, it ought to work even better. Well, the first thing that became very obvious with my first ride on the Mini was the bounciness - I really had to concentrate very hard not to bounce a lot. So the first thing I did was to investigate the mechanism with a view to tightening the suspension screw which Yan mentioned once. But that did not change the spring constant - all it did was to move the end stop. So that didn't work. So I next implemented BruceMetras' solution of replacing the spring with an elastomer. Once I got the right elastomer in there, bounciness was much improved.
Unfortunately, much of the suspension's ability to absorb bumps was also lost. It still takes the edge off bumps but nevertheless is now is a harder ride than the Raleigh 20. And the other thing that has come out, while bounciness is much better, it is not gone. I still have to pedal at a lower cadence than my optimum to avoid pogoing on the saddle. Not so with the Thudbuster. I can pedal as fast as I want with no bouncing. Plus it is much smoother.
So apologies for this lengthy post, but now I wonder if this bounciness would be a problem with all bikes with rear suspension? If so, then for the sort of riding I do, a Thudbuster is a better option despite the sprung mass being much higher.