So you've determined that your line quality sucks. Here are some things that you can do to try to fix things.
First, let's assume that I know what I'm talking about, because I do. I'm posting these things here because they work. If you can't accept that, then go away.
You might be wondering what all the baking goods are for... it's a little home chemistry. The meaning will become clear.
Unplug all telephone devices that are connected to the line in question. Remove the wall plate. Attach your voltmeter to the pair you're testing, observing the following polarity:
Go outside to the terminal block where the telco lines connect to your house. Disconnect the pair you were testing from the block and test the voltage. If you still don't have 48 volts (or very close to 48 volts) there's a problem on the telco side and you'll need to have them check your line. If you do have 48 volts and you don't inside your house, there's a problem inside.If your polarity is reversed (see above), reverse the order of the incoming telco wires. If you'd rather not muck about with telco wiring, you can alternately just reverse the wires of the pair on the jack inside.
While you're out here, dust the terminal block with baking soda and pour on a little water. This will neutralize any corrosion on the terminal block. Rinse with a little alcohol to prevent water damage.
This is the fun part. Mix in some salt with a little white vinegar. Now dip the copper end of the wire in the solution. This will dissolve any corrosion. Use a cotton swab to rub the wire to remove any stubborn corrosion.
Immediately rinse the wire with alcohol to prevent accelerated corrosion as a result of the vinegar/salt solution. The wire should now be a bright, shiny copper color, not a dull brown color.
Clean each of your outside wires using the copper cleaning method described above. Do this one wire at a time so you don't get polarity confused. Resecure each wire tighly, but don't overtighten any of the terminals; this can weaken the wires.
For each wall plate inside your house, remove the plate and clean each of the wires, using the method described above. If corrosion is present on the terminals of the wall jack, replace the jack. It is best to replace the jack with one that has gold plated terminals.
Take a look on the front side of your faceplate. Make sure that the 4 pins inside the jack are shiny and not corroded. It might help to use a bright light and a magnifying glass here. If there is any corrosion, replace the jack.
It is common for wall plates to be used as junctions; each terminal may have a pair of wires connected to it. If this is the case on a terminal, make sure that pair are like-colored (eg, red with red, green with green, etc). Make sure the connections here are good; this can be an excellent place for noise to creep in.
Now would be a good time to recheck the line voltage if it was low before. If your indoor voltage still doesn't match your outdoor voltage, you may have additional terminal blocks in your attic. If you don't have additional terminals in the attic, you may need to replace your interior wiring, or wire in another cable for your modem line. If you add new wiring, make sure that if the phone line has to cross any other cabling in your house it crosses at a 90-degree angle to prevent noise creeping in by induction.
Unplug the base cable that goes from your modem to your wall jack. Hold the ends next to each other so that the connectors are facing the same way (ie, both prongs up or both prongs down). The red and green wires should be reversed from one end to the other. If this is not the case, either replace one connector (if you have the necessary tools) or replace the cable.
Now plug the cable into a regular telephone and hit a number to cancel the dialtone. Wiggle the cable just in front of each connector. If you hear static as you do this, replace the connector or the cable. Be sure that if you replace the connector, you observe reversal of the red/green wires from one end to the other.
Secure all wall jacks, plates, etc. You may now notice an increase in line quality and associated connect speeds. Begin plugging in other telephone equipment (phones, answering machines, etc) while continuing to test the line with your modem. If you notice a sudden drop, suspect a problem with the piece of equipment you just plugged in.
If you're still having problems, give the telco a call and tell them you're having problems faxing. If you tell them you're having modem problems, they won't really care.