Since Irfanview version 4.20 there's been a plugin that enables doing exactly what I was looking for -- reducing the filesize of a jpg to whatever size you want.
So thanks for your suggestion!
FWIW here's my write-up of how to do it, or rather how I did it for several different jpg's that needed to have their filesizes reduced to just under 1 MB:
Reducing a jpg file size efficiently:
Use Irfanview v4.20 or later with all plugins
Open image in Irfanview
File > Save for Web ... (Plugin)
Info msg opens: "This file contains a high resolution image. RIOT can handle such images, but processings can be quite slow in this situation"
"Do you want to resize it first? (Recommended)
The original image will not be modified."
Click on Yes.
Don't change image dimensions unless you want to, but do the Resampling with the Catmull-Rom resampling filter, by clicking on OK.
A new window opens showing the original image on the left and the new image on the right.
You don't need to move the Quality slider.
For Chroma subsampling, select high.
Click on Compress to size.
A small "Compress to Size" input box opens.
Enter the file size you want in Kilobytes and click OK.
Wait a few seconds till processing has finished.
Then File > Save As (new filename unless you want to overwrite the original image).