Conspiracy is an agreement to commit an offence plus an intention that the offence should be committed by one or more of the conspirators. This means that recklessness as to whether or not the offence is committed is not enough: there must be an intention that it will be committed: R v LK; R v RK  HCA 17 (26 May 2010).
When I summarise it so simply, the position seems obvious. How could it possibly be argued that D is conspiring if he is only reckless as to whether the full offence is committed?
In the appeals in LK and RK the alleged full offence was dealing with money while being reckless as to whether or not it was proceeds of crime. So, on the alleged conspiracies, why wasn't it enough for Ds to agree to deal with the money while intending that they should be reckless as to whether the money was proceeds of crime?
Intending to be reckless, in this context, is the same as being reckless as to whether there is an agreement to commit the offence. Therefore it is insufficient for conspiracy.
The joint judgment of Gummow, Hayne, Crennan, Kiefel and Bell JJ (and Heydon J agreeing at 145) puts it like this at 122:
" ... At the time the agreement was made the money may, or may not, have been (or have become) proceeds of crime. The agreement, if carried out in accordance with LK's and RK's intention, may not have involved a dealing with money that is proceeds of crime. It follows that, on the evidence given at the trial, it was not open to find that either respondent intentionally entered an agreement to commit the offence that is said to have been the object of the conspiracy."
French CJ said much the same thing at 77:
" ... There cannot be a conspiracy in which the parties to the agreement are reckless as to the existence of a circumstance which is a necessary element of the offence said to be the subject of the conspiracy. Such recklessness would be inconsistent with the very intention that is necessary at common law and under the Code to form the agreement alleged. In this case that intention is an intention to deal with money which is proceeds of crime. Recklessness as to whether the money is proceeds of crime is recklessness about a term of the agreement constituting the conspiracy...".
The Chief Justice leaves it to law students to work out whether his reasons on this point are the same as those of the other justices.
And, while you can't recklessly conspire, you can conspire to be reckless: Ansari v R  HCA 18 (26 May 2010). In LK there was recklessness as to recklessness, and no conspiracy, whereas in Ansari there was intention to be reckless, and a conspiracy. The mens rea for conspiracy must be kept separate from the mens rea for the full offence. Whatever the latter may be, intention to commit the full offence is required for the conspiracy.