How to plot outline of overlapping circles

Dear List,

I'm plotting circles depicting the same distance around a given coordinate representing the range of a VHF transmitter. While these VHF transmitter sites are usually quite close together to get a seamless coverage, there are obviously no sites in the middle of the sea. I'm interested in the visual representation of the coverage. I'm not interested in the exact coverage of each and every single transmitter, just in the boundary where the coverage ends. 

Currently I'm plotting the coverage with the build in ellipse symbol (-SE) getting overlapping circles (see output.jpg; the thick white lines). I'd like to reduce the circles to the part crudely highlighted in red in desired_result.jpg representing the outer boundary of the covered area and get rid of any parts laying inside the covered area.

I have currently no idea on how to achieve the desired result. Any nudge in the right direction is greatly appreciated.

All the best,
Kristof Koch

I'm currently using 

gmt - Version 5.1.0 (r12452) [64-bit] on 
Ubuntu 12.04.3 LTS (GNU/Linux 2.6.32-042stab081.5 x86_64)

The part of the script generating the white circles in the attached images:

cat > $WORK_DIR/com_site.txt << END
-22.606 63.985 0 1111.2 1111.2
-19 63.4 0 1111.2 1111.2
-7.588 62.107 0 1111.2 1111.2
END

psxy \
	$WORK_DIR/com_site.txt \
	-J -R \
	-SE -Wfat,white \
	-K -O \
	>> $FILE




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