more MySQL issues

I thought I had things figured out from the last msg from George. But
when I got back on this morning, I see I can get into the mysql DB
without a password as a regular user (me, pete). Also, in webmin, I can
easily see everything too. The password for the DB is different from my
regular root password, but still no prompting. Here's the output from
this morning:

[pete@rotor pete]$ mysqlshow
+-----------+
| Databases |
+-----------+

| Phoenix   |
| mysql     |
| test      |

+-----------+
[pete@rotor pete]$ mysql
Welcome to the MySQL monitor. Commands end with ; or \g.
Your MySQL connection id is 22 to server version: 3.23.55

Type 'help;' or '\h' for help. Type '\c' to clear the buffer.

mysql> use Phoenix
Database changed
mysql> show tables;
Empty set (0.00 sec)

mysql> use mysql
Reading table information for completion of table and column names
You can turn off this feature to get a quicker startup with -A

Database changed
mysql> show tables;
+-----------------+
| Tables_in_mysql |
+-----------------+

| columns_priv    |
| db              |
| func            |
| host            |
| tables_priv     |
| user            |

+-----------------+
6 rows in set (0.00 sec)

mysql> select User,Host,Password from user;
+------+--------------------------+------------------+

| User | Host                     | Password         |

+------+--------------------------+------------------+

| root | localhost                | 77f55a9e14442c8f |
| root | rotor.byerlyelectric.com | 77f55a9e14442c8f |

+------+--------------------------+------------------+
2 rows in set (0.01 sec)

mysql>


With only root in the DB I would think I'd be prompted each and every time.

pete