Process Improvement versus Process Automation. What should come first?

Following my most recent post, I have received a number of questions which involve a confusion over the difference between BPM and Workflow. I would like to cover that in a subsequent post but embedded in the feedback, is also the question: What should come first - Process Improvement versus Process Automation?
Coincidentially this mirrors a discussion that is currently ongoing within one of the BPM groups on LinkedIn.
Here is my view of the answer to this question.
I would strongly suggest and recommend that Improvement should always come before Automation. Some manual processes may well only require manual improvements without the need for automation. Additionally depending upon the nature, scope and scale of the process in question, the business case for automation may not stack up as Cost may well be > the Value to be derived from the automation.
Improving a manual process may well be the best option - Business Process Management [and Improvement] does not always mean automation, workflow etc.
May I acknowledge Rachael Ovett [BPM Consultant] for this Bill Gates quote on automation, but I think it sums it up well:
"automation does not fix the errors, it just makes them happen quicker".
I accept that process improvement may be bourne out of automation but common sense must lead one to the conclusion that fixing the errors first, must be the priority!