One unnatural fear that many beginning to intermediate Omaha players have is being quartered.  "Being quartered" means that you tie another player for half the pot and they win the other half of the pot outright.  For example, let's say you hold the following Omaha hand:

Ace of Clubs Three of Diamonds Nine of Diamonds Nine of Hearts
Hole Cards

and the final board is showing

Jack of Clubs Two of Hearts Seven of Diamonds   Six of Clubs   Queen of Hearts
Flop   Turn   River

In this particular hand you have the "nut low" (A2367) and a pair of 9's for high.  If you are up against this hand

Ace of Diamonds Three of Clubs Seven of Clubs Six of Diamonds
Hole Cards

then you will only get 1/4 of the pot because they also have the nut low and in addition they have two pair (7's and 6's). Because of this situation many players play their nut low very timidly through the hand for fear that they will be quartered. This is often incorrect.

If you have the lowest low hand possible and any high hand at all, it is often in your best interest to play the hand very aggressively from start to finish, especially when there are more than two people in the pot which is almost always the case in low limit Omaha. The reason for this is that, while you may be quartered you will often lose very little from this by the end (sometimes even making money on a quartered hand), however when you quarter someone else you stand to make a very good profit (second only to scooping). A hand like

Ace of Diamonds Two of Diamonds Three of Clubs Four of Clubs
Hole Cards

would play the above hand very strongly on each round because they have an uncounterfeitable low (any low card besides a 2 or 7 gives then the nut low hand after the flop) however on the river your high hand (combined with your nut low) will give you 3/4 of the pot.

When To Slow Down

Sometimes it is correct to slow down when you have a nut low and weak high hand.  This is especially true if you find yourself on the flop and turn with only a single opponent.  In this case it is better to simply call them down since the penalty for being quartered is much higher when you don't have other players in the hand with you.  Even with just two players besides yourself in the hand it is usually correct to play a nut low and weak high hand strongly.