SQL & PL/SQL

I tried to figure out how "connect by level" clause works, but I am not able to come up with how it works.
As a try-out, I created a table with 3 column "from_date" date type, "to_date" date type and "user_name" varchar type.
It has 2 rows:

FROM_DATE   TO_DATE     USER_NAME
------------------   --------------   ------------------
15-OCT-09     18-OCT-09   thomas
25-OCT-09     30-OCT-09   jane

Upon executing the following SQL:

SELECT DISTINCT level - 1 + from_date "DAY", user_name
FROM my_table
CONNECT BY LEVEL < (to_date - from_date + 1)
ORDER BY user_name;

I get the following results:

 LEVEL      DAY            USER_NAME
-----------   ----------------   ------------------
         1    25-OCT-09   jane
         2    26-OCT-09   jane
         3    27-OCT-09   jane
         4    28-OCT-09   jane
         5    29-OCT-09   jane
         1   15-OCT-09   thomas
         2   16-OCT-09   thomas
         3   17-OCT-09   thomas

[This is an exact presentation that I am looking for]

But, if DISTINCT is ommitted, query returns many rows as follows:

LEVEL      DAY            USER_NAME
-----------   ----------------  -----------------
         5    29-OCT-09   jane
         4    28-OCT-09   jane
         3    27-OCT-09   jane
         5    29-OCT-09   jane
         4    28-OCT-09   jane
         2    26-OCT-09   jane
         5    29-OCT-09   jane
         4    28-OCT-09   jane
         5    29-OCT-09   jane
         3    27-OCT-09   jane
         4    28-OCT-09   jane
         5    29-OCT-09   jane
         2    26-OCT-09   jane
         4    28-OCT-09   jane
         5    29-OCT-09   jane
         3    27-OCT-09   jane
         4    28-OCT-09   jane
         5    29-OCT-09   jane
         1    25-OCT-09   jane
         4    28-OCT-09   jane
         5    29-OCT-09   jane
         3    27-OCT-09   jane
         4    28-OCT-09   jane
         2    16-OCT-09   thomas
         3    17-OCT-09   thomas
         3    17-OCT-09   thomas
         3    17-OCT-09   thomas
         3    17-OCT-09   thomas
         2    16-OCT-09   thomas
         1    15-OCT-09   thomas

So, how do I eliminate duplicates in "level" column within same "user_name" without using DISTINCT (as it requires sorting). And my production db has many many rows the table that I have to work on and my application invokes this query many times. So, its unimaginable to think of resource usage by way of using DISTINCT. Does any expert have a workaround for this? I'd like to eliminate GROUP BY, DISTINCT clause and use any alternative light-weight clause instead.
Help is highly appreciated.

Regards,
...