It was a turbo tournament with blinds increasing every 15mins and apart from the small stack the stack levels involved with the hand were about 10,000 and 9,000 which was probably just above the average stack. At this point the blinds were 500/1000.

What would the best play be in this situation, and what would it be in a more deepstacked, slower levels tournament with about the average stack?

Both times they have just abit less than me

After I had called the raise I had about 5000 left the first tiime, and 8000 left the second time.

[Which way do you think the best way to play the hand is, and how would you play it?]

I'm dealt  K in the BB. The under the gun player raises to 3xBB, an another player moves ALL-IN for an extra 1000 when the blinds are 400/800. I decide to call and so does the original raiser. On an 8 high flop i move ALL-IN, and the under the gun player folds.  on the turn and  on the river means i won the hand.
The under the gun player folded  , and the ALL-IN player  .

Later in the night I'm dealt  again and its limped to me in the SB. I call the 1000BB and raise another 2000. The BB folds and a small stack moves ALL-IN for another 600. One more player calls and i knew that he didn't  have  from his hesitation. I then moved ALL-IN which put him all in for about another 7000. He called showing    , and the short stack showed  . The flop came 7 high but the  on the turn meant  lost the hand, and left me with hardly no chips to play with.

Which way do you think the best way to play the hand is, and how would you play it?