Access denied trying to add a computer alias

Hello,

Running netdom computername <COMPUTER> /add:<ALIAS> as domain admin I got "Access denied". I have verified the user has full control on msDS-AdditionalDnsHostName for <COMPUTER>.

What puzzles me is the DNS entry is not created but netdom computername <COMPUTER> /enum shows <ALIAS> in the name list, but msDS-AdditionalDnsHostName is set to <none> (I don't know what value must hold after a successful /add)

netdom computername drogon /add:drogon1.domain.local
Unable to add drogon1.domain.local
as an alternate name for the computer.
The error is:
Access is denied.
The command failed to complete successfully.

netdom computername drogon /enum
All of the names for the computer are:
drogon.domain.local
drogon1.domain.local
The command completed successfully.

Thank you in advance.