Sitelinks demotion: will this work?

Hi, I have this client site which have very few pages (just 9). Google is showing 8 sitelinks right now (pages A, B, C, D, E, F, G and H). Now the client says he would like page "I" to appear as a sitelink.

I told him that the sitelinks are algorithmically selected and one can't chose but I've been thinking about this: what if I demote sitelink H? Is there a proability that Google starts to show a sitelink to page "I" because H is demoted?