Add/remove sprockets on cassette to customize gear ratios I have a Shimano 105 10-speed cassette on my road bike, with sprockets 11-12-13-14-15-17-...-28 (I don't know by heart what comes between 17 and 28). I'd like to remove the 11, and put a 16 between the 15 and the 17 (because I dislike the gap between 15 and 17, and I don't use the 11 very much). I can find the sprocket: this one is for Ultegra, but I suppose it should work for my 105 too (http://www.rosebikes.nl/artikel/shimano-ultegra-cs-6600-10-speed-tandwiel-met-16-tanden/aid:119171). 

Can I just take 11-15 off, put 16 on, then put 12-15 back on? Or is there something else I need to consider?

Alternatively I'm willing to buy another cassette instead, but I don't want to give up the 28. Are there compatible 10-speed cassettes available with 12-13-14-15-16-17-...-28 (or possibly even 29 or 30)?
If you want sram cassette (which should be compatible):
Sram PG1050 and PG1070 come in a 12-28 configuration matching what you need
12-13-14-15-16-17-19-22-25-28

https://www.sram.com/sram/road/products/sram-pg-1050-cassette
https://www.sram.com/sram/road/products/sram-pg-1070-cassette

If you want shimano
Buy two Shimano 105 ten speed cassettes (well, you already have one, so you're half way there). The 12-25 version has a 16t cog and the 11-28 has the other cogs you will need. Might be able to find a used cassette that has the cog you need.

Here's the options for Shimano 105 CS-5700 series
11-25 = 11-12-13-14-15-17-19-21-23-25
11-28 = 11-12-13-14-15-17-19-21-24-28
12-25 = 12-13-14-15-16-17-19-21-23-25
12-27 = 12-13-14-15-16-17-19-21-24-27  

See Shimano 105 cassette details:
http://bike.shimano.com/content/sac-bike/en/home/road/drivetrain/cassettes0/cs-5700.html

Shimano Tiagra Range has a 12-30 cassete, but it also does not have a 16t cog.
12-13-14-15-17-19-21-24-27-30T