confirmed – got my hosting provider up the value from 2M to 8M: no problems anymore!
1) if you have control over php.ini, or any way to add settings to it, change upload_max_filesize to at least 3M
2) you will find a lot of articles claiming these settings can be controlled by entries in .htaccess or by adding ini_set lines in your php code – didnt work for me
3) last resort:
replace
<?php echo min((floor( wp_max_upload_size() * 0.99 / 1024 / 1024 ) - 1), 8); ?>
with
a number , e.g. 2, 5, 10 (designates MBytes max file upload size)