What are the characteristics of a "good" smoothing convolution kernel? At work we were smoothing a signal by convolving with either

f1=[0.2000 0.2000 0.2000 0.2000 0.2000]


or

f2=[0.1111 0.2222 0.3333 0.2222 0.1111].


A colleague noticed that f1 smoothed "stronger" than f2 and suggested a new filter:

f3=[0.2727 0.1818 0.0909 0.1818 0.2727] 


His reasoning was that this should smooth even "stronger" than f1, and therefore be better.

My answer to this was that 


if he wanted "stronger" smoothing he should instead increase the
size of the filter 
a good smoothing filter should always approach zero at the start and beginning


My motivation for 2. was Gaussian filters which are often used for noise reduction in image analysis.

Is 2. correct?

Also because of the periodic nature of DFT does not f3 have the same frequency response as

f4=[0.0909 0.1818 0.2727 0.2727 0.1818],


which in turn should have a very similar frequency response as f2?

Edit: I followed Jim Clay's suggestion and zero padded and the result shows that f3 has terrible stop band ripple while f2 is quite OK in  this respect:


Thanks in advance for any answers!
Yes, in general, your #2 is correct.  That being said, both of the filters stink (with your triangle filter being a little better).

No, f3 does not have the same frequency response as f4.  To get an idea of why that is so, you generally have to zero-pad the impulse response before DFT'ing it to get a reasonable idea of what its frequency response looks like.