First off, tape hiss isn't "random noise". It is quite consistent every time to press play on the machine. It is caused by the tape running over the tape head. Faster tape speeds move the frequency range that the hiss happens at up higher. Cassette's run at relatively low speeds, thus, the tape hiss is well in the audible range for all humans. About the slowest speed that tape hiss is not audible is 30IPS (inches per second), and you won't find any cassette players/recorders that run tape that fast. Thus, you have noise reduction.
Noise reduction is a sort of compression scheme that only compresses the lower frequencies while recording to tape. By doing so, you are able to record much hotter levels of high frequency to tape which is what helps eliminate tape hiss. When a recording that was recorded with some type of noise reduction ("encoding") is played back, the "decoder" expands the bass back out so that the overall frequency range is mostly unchanged from where is started out. The success of the noise reduction in not only eliminating hiss, but also not drastically changing frequency response is dependent of how well the manufacture built the noise reduction circuit as well as many other factors. But let's say for the sake of arguement that most noise reduction scheme's on newer recording equipment works well enough for the price point of the product. While the dbx on your unit is FAR from state-of-the-art noise reduction, your unit is far from needing higher quality noise reduction, because traditionally, 4 track cassette recorders are used for demo purposes. On a demo, sacrificing a little frequency response, or having a bit of tape hiss even WITH noise reduction on is acceptable.
Anyway, if you RECORD with noise reduction, you need to PLAYBACK with noise reduction too. You will notice that music that was "encoded" with noise reduction with actually sound like it has MORE hiss if you play it back without the same type of noise reduction "decoding" it.
Now, it is debatable, and subject to much arguement whether noise reduction on a cassette helps or hurts the overall sound. Try recording both ways to see which offers the most benefits to your recordings.
A little tip though. Most "demo" recordings always seem to suffer from overhyped up low midrange frequencies in it. While you are tracking, you need to really try to clear this up because all that lower midrange is eating up headroom on the tape, thus, you cannot achieve as hot of recording levels as you would like. The hotter the signal you can record to tape the less you will notice tape hiss is the rule. So, try to achieve the hottest levels possible while tracking to cassette tape to overcome tape hiss. If the tape hiss is still unacceptable, then employ your noise reduction to help reduce tape hiss.
Good luck.
I have had some luck using software plugin's to eliminate tape hiss on recordings transferred to a computer. Steinberg's Denoiser VST plugin seems to work quite well at eliminating tape hiss without changing the sound of the music very much. I have done a little bit of audio restoration on cassettes in the past, and all the clients were quite pleased with how Denoiser worked. So, you might check it out, along with the many other noise eliminating plugin's that are available.
Ed