Order of authors in an engineering publication Recently, I was involved in an engineering research project where I significantly extended the main functionality of the work. As my other team-mates were not involved in that aspect of the project, I thought I would leave them to do the write-up. I don't want to complicate things but lets just say their contribution matters less, at least according to my advisor.

This work is now being readied for publication and there's the matter of ordering the authors. Initially I thought we may be doing things alphabetically, but on the recent draft the order appeared to prioritize those who are doing the write-up, listing them first. My advisor raised no objection to this. If we are going down this road, it seems to me those who have done the most work should be first authors (i.e. me), rather than those who are doing the write-up.

I'd like to avoid any potential conflict with the people involved, and so I wonder if one acceptable compromise here is to specify the contributions of each author in the paper. Alternatively, we can do the alphabetical thing and make explicit mention of this as a footnote. I don't have any problem with either of these options.

First, am I correct in thinking that the ordering here is misplaced?

Second, are the compromises I list reasonable enough to propose?
You must discuss this issue with your advisor and all coauthors as soon as possible.  The right time to have the discussion would have been before the first draft is started, but unless you have a time machine, you have to have it now.  Since there are differing opinions, and the outcome matters, conflict is inevitable.  Welcome to adulthood.