As per LV's idea, I'm going to walk you through how to reduce stuttering to an lower level. The process involves altering three separate things, and I'll try and make it as easy to follow as possible.

Bare in mind that this is merely a guide, and you may experiment to find settings that suit you better (i.e. a higher resolution than recommended here).
Step 1 - Reducing Sound Overheads
Reducing the sound overhead on your CPU can lower audio and graphical stuttering. To reduce the amount of pressure that your sound card/onboard sound is putting on your CPU, follow these steps.
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Press Start, then navigate to the Control Panel. Once there, you are looking for the Sounds and Audio Devices icon (as shown above).
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Once opened, the Volume tab should be shown automatically. Press the Advanced button under Speaker Settings, to open the Advanced Audio Properties window.
Once here, select the Performance tab at the top, and slide the Sample Rate Conversion Quality slider all the way to the left, so that it shows Good, rather than Best. Once done, press OK, and then OK again to close the Sound and Audio Devices window.
That's it for step 1!

Step 2 - Configuring the Graphical Options within X3:TC
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This is an easy one. Fire up X3:TC, so you are presented with the splash screen as shown above.
Press the Graphical Settings button, and set Texture Quality, and Shader Quality both to Medium using the corresponding drop down boxes.
Make sure to disable Antialiasing and Anisotropic Texture Filtering by unchecking the check boxes above.
Set your resolution to the lowest possible using the Resolution drop down box. The lowest here is 1024x768.
Step 2 done and done!

Step 3 - Stop the In Game Bill Boards Displaying Movies
Some users have experienced a decrease in stuttering by disabling the in game bill boards that work by continually accessing data stored on the hard drive. Disabling them stops the data being accessed, and decreases stuttering.
To disable the billboards, you need to navigate to where X3 Terran Conflict is installed on your computer. By renaming the file that the bill board videos are located in, X3:TC will not be able to find them, and thus will not play them.

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Steam Users
Assuming you have used the default install options for Steam, X3:TC is installed to X:\Program Files\Steam\steamapps\common\x3 terran conflict, where X is the hard drive Steam is located on.
Use Windows Explorer to navigate to said Steam folder.
Once there, access the mov folder, and locate a file called 00002.dat. Right click on the file, and select Rename.
Add something to the end of the file name, such as _old, so the file name now reads 00002_old.dat. In the example above, LV added text to the filename to explain why it was renamed. Close the window, and you're done!
DVD Users
Apologies if this is wrong, as I do not have the DVD version of X3:TC (so a mod may need to correct this

X3:TC is installed by default to X:\Program Files\Deep Silver\X3 Terran Conflict. Navigate there using Windows Explorer.
As with the Steam version, once there, access the mov folder, and locate a file called 00002.dat. Right click on the file, and select Rename.
Add something to the end of the file name, such as _old, so the file name now reads 00002_old.dat. In the example above, LV added text to the filename to explain why it was renamed.
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Bob's yer uncle. Fire up X3, and give it a whirl to notice the difference.

Phew - Cheers to LV for the pictures, homerdog for spotting the bill board issue, and Elucca who spotted the Medium textures fix. Apologies if this doesn't make sense, it's 2am.
