Disclosed herein are computer-implemented methods and systems for securely carrying out electronic transactions including electronic drafts, wherein payment on at least one of the drafts is contingent upon the removal of an associated contingency. The method may include steps of establishing a secure computer site accessible only by authenticated parties to the transaction and by any authenticated contingency approver. The site includes a representation of the transaction that includes a representation of each of the plurality of drafts and an option to remove any contingencies associated therewith. Parties and contingency approvers requesting access to the computer site are authenticated by encrypting identification information provided by the requesting party or contingency approver over a secure channel and successfully matching the encrypted identification information with an encrypted identifier that is stored by a bank, the encrypted identifier being unique to the requesting party or contingency approver. Payment on the constituent drafts of the transaction are released by the bank only when the option to remove each contingency associated with the draft is timely exercised by an authenticated party or authenticated contingency remover that is authorized to remove the contingency. Complex transactions may thereby be carried out securely, remotely and without compromising personal and/or financial information. The invention obviates the need to disseminate identification surrogates such as credit card numbers over public networks as well as the need to rely upon in-person holographic signatures on paper documents for authentication purposes.