Debian :: OpenJDK And Icedtea - Plugin Conflicts

I have the following packages of openjdk and icedtea installed.
i openjdk-6-jre - OpenJDK Java runtime, using Hotspot JIT
i openjdk-6-jre-headless - OpenJDK Java runtime, using Hotspot JIT (headless) 
i openjdk-6-jre-lib - OpenJDK Java runtime (architecture independent libraries)
i icedtea-6-jre-cacao - Alternative JVM for OpenJDK, using Cacao
i A icedtea-6-jre-jamvm - Alternative JVM for OpenJDK, using JamVM

Now I am not a developer or anything just a user. My use-case are two :-
a. Running java programs on the desktop
b. Running java in the web-browser.

I *think* both of them get installed by default. Openjdk via the default-jre virtual package while icedtea due to some of the openjdk headless packages.
~$ aptitude why openjdk-6-jre
i default-jre Depends openjdk-6-jre (>= 6b23~pre8-2~)
~$ aptitude why icedtea-6-jre-jamvm
i openjdk-6-jre-headless Recommends icedtea-6-jre-jamvm (= 6b23~pre8-2)
~$ aptitude why openjdk-6-jre-headless
i openjdk-6-jre-lib Depends openjdk-6-jre-headless (>= 6b17)
$ aptitude why openjdk-6-jre-lib
i openjdk-6-jre-headless Depends openjdk-6-jre-lib (>= 6b23~pre8-2)

Notice the circular dependency at the end. From what I read the headless packages are basically for those systems where a server is running which does not have have a monitor, in which case I wonder why its installed in my system? My actual issue is of having the java for iceweasel. I did search for having java plugins and did not find anything except for icedtea-plugin to run java on my browser.

Trying to install it through gave conflicts :-
$ sudo aptitude install icedtea-plugin
[sudo] password for shirish:

The following NEW packages will be installed:
icedtea-netx{a} icedtea-plugin xulrunner-1.9.1{ab}
0 packages upgraded, 3 newly installed, 0 to remove and 4 not upgraded.
Need to get 8,642 kB/9,103 kB of archives. After unpacking 26.5 MB will be used.

The following packages have unmet dependencies:
openjdk-6-jre-headless: Conflicts: icedtea-netx (< 1.1.1-2~) but 1.1-1 is to be installed.
xulrunner-1.9.1: Depends: libmozjs2d (= 1.9.1.16-6) but 1.9.1.16-9 is installed.
The following actions will resolve these dependencies:

Keep the following packages at their current version:
1) icedtea-netx [Not Installed]
2) icedtea-plugin [Not Installed] 
3) xulrunner-1.9.1 [Not Installed]

Accept this solution? [Y/n/q/?] q
Abandoning all efforts to resolve these dependencies.
Abort.

I did see the other solutions but most of them recommend downgrading both the openjdk and icedtea packages to the ones in testing rather than in unstable.