Define a test directory.
Access the Security dialog in the properties of
this new directory.
Here grant Users Modify, which will automatically
check all of the boxes below Modify. Now, uncheck
Modify, which will leave all of the boxes below Modify
still checked. If you click on advanced now you will see
that Users are grant Read, Write, Execute of This folder,
subfolders, and files. If you look at the details by highlighting
that grant in the Advanced view and clicking edit you will
see that a number of things are included in the grant, but that
both of the deletes are not included.
If you want some other group that Users to have this ability
then use that group. However, remember that the permissions
that an account has is the sum of permissions granted to it and
all groups that it is in.