Or you can use Leadership, if you find that there are some rules lawyers in your group that are insisting that because the Initiative SC states that you do not get a Strategic Action this turn, that it is inclusive of any Strategic Action that you are allowed to take. You may not have a use for secondaries that come around (either because of the timing that the SC was played, or your current situation, anyways. Leadership gives you the power to put CCs not only in the Strategy Alocation area (which is essentially what Initiative does), but in your Command Pool or your Fleet Supply also. If you, again, are able to get both 1 (Leadership) and 4 (Logistics) you could be looking at 12 command counters (including the 2 you normaly get) which is your full complement of counters, not to mention, everyone else will only be able to get CCs if they have the influence when you play your SCs. Personally, I don't see the need in taking both 1 and 4 for all those CCs, as you will no doubt have at least a few on your sheet in your fleet supply anyways, so some of it might be wasted, unless you time it properly. I would suggest using 4 first, as the secondary requires you to pay more, though some players that have alot of influence heavy planets could really benifit, as there is no cap, unlike 1.
Another nice thing about having Logistics AND Leadership in the game, is that you will have a much more eventfull game, as people are going to be able to perform more actions each round. If you are also using Warfare I, you also get that nice double use CC, which can make your counters go furthur.
An alternative to using only the lowest number of the two SCs that each player has chosen, is to instead progress through the turn order for all eight cards. So if a player takes 1 and 2, they will get two consecutive turns (1 and 8 will also give this result, last and first). This can give a bit more tactical interaction than simply choosing a low number SC, and the SC that you really want/need.
If you do switch out Initiative for Leadership, I do suggest switching Politics over to Assembly, so that the Speaker Token still moves around through the players. If you don't make the switch, either have a roll for the ST, or have the ST move one player left or right (your choice) to keep it moving around.
Switching around your SCs can really have a neat effect on the game. Have fun with it, see how people in your group play, and switch them around accordingly, so that you and your group can all get the most out of the game! Keep it fun, Keep it new, Keep it challenging!