8 Teams 10 Games

[annagram]

Apologies if this is already out there--I couldn't find it. 

I organize a Lawn Games Decathlawn every year, with 10 games, but this year we only have 8 teams. I'm trying to figure out how to make a fair schedule. All teams should play each game once. All teams should also play each other team at least once, though with only 8 teams, I know some matchups will be played twice. 

We might also end up with 9 teams, which I assume means each team will end up with a bye round due to the odd number of teams. 

Help?

[Ian Wakeling]

It is possible to make it work with 8 teams (A to H).  In the following every team has played each other team once when the 7th round (row) is complete, so the repeated matchups are all in the last three rows.

(---) (G A) (---) (D H) (---) (E F) (---) (B C) (---) (---)
(---) (---) (C D) (---) (E A) (---) (H F) (---) (B G) (---)
(---) (---) (---) (B E) (---) (C H) (---) (F A) (---) (D G)
(B D) (---) (---) (---) (C F) (---) (E G) (---) (H A) (---)
(---) (E C) (---) (---) (---) (D A) (---) (H G) (---) (B F)
(C G) (---) (E H) (---) (---) (---) (B A) (---) (D F) (---)
(---) (B H) (---) (G F) (---) (---) (---) (E D) (---) (C A)
(H F) (---) (B A) (---) (G D) (---) (---) (---) (E C) (---)
(---) (F D) (---) (A C) (---) (G B) (---) (---) (---) (E H)
(E A) (---) (G F) (---) (H B) (---) (C D) (---) (---) (---)

I cannot see any nice solution for 9 teams, because of the odd number of teams, the byes and the impossibility of giving teams the same number of games.  It's better to avoid the problem somehow.