Here is a playing insight that I have never read about. Steven Burns introduced me to it (he learned about it in France.)
Clean playing comes as a result of focused a centered focused embouchure: accurately buzzing the desired pitch. Valve changes must be clean. All keys must be practiced (scales, chords, and intervals - at all dynamics and articulations.)
When all these basics are mastered somewhat there remains and advanced topic: It can be called an against the grain pitch change- (the concept is used by trombonists all the time.)
"With the grain" would be moving to shorter tubing while going higher C# (1,2,3) to G (0). This type of interval does not present undue problems - just hear it and play it, with normal clean fingerings.
"Against the grain" would be "low" C (0) to C# (!,2,3). Going from the open horn to the longest amount of tubing available. Even when the fingerings are clean, accurate, and fast - a turbulence is created by the lengthening of the air path through the horn. Common problems occur in the trill between third space C and the D above it (0 - 1), as in the Carnival of Venice, first Variation.
This against the grain phenomenon occurs frequently - (C - D) (C - E) (C- F) ... (D -Eb) ... (F# -G#). They happen in every scale.
Once made aware of this, the player will notice this every time it happens. It tends to harm lyrical passages in most players performance. It is where the unwanted noise crops up - when nothing wrong has been done - and the mastery of this is what separates the Maurice Andres from the mass of players - who are unaware of it most of the time.
The solution to this is to practice slow trills on every instance of this. Play your circle of fifths, trilling every across the grain slur. Do now move on until it is clean and clear. It can be done, and is a matter of air and embouchure coordination.
Have you ever experimented with this?