Short answer. Yes. Rule 23, Section 16 lets you move the court, for good cause shown, to order that the deposition be held with no one present except the parties and their officers or counsel. The court decides after your motion and can grant this along with other protective orders shielding you from annoyance or embarrassment.
What the law says
That the scope of the examination shall be held with no one present except the parties to the action and their officers or counsel
Rule 23, Section 16 — Orders for the protection of parties and deponents. Read the full provision →
Ask for a protective order before the deposition
A deposition by oral examination is normally open to the parties, their lawyers, and whoever else has a legitimate reason to attend, such as a stenographer. If you want that changed, Rule 23, Section 16 lets any party or the person to be examined file a motion, but it has to be seasonably made and supported by good cause shown — the court will not restrict attendance just because a party finds it uncomfortable to be watched.
The specific order the rule allows
The rule lists several protective orders the court may issue after such a motion, and one is written for exactly this situation. That the scope of the examination shall be held with no one present except the parties to the action and their officers or counsel. Framed this way, the order does not cancel the deposition — it simply narrows the room to the litigants and their lawyers, cutting out observers who are not part of the case.
Other protections available in the same motion
Excluding outsiders is only one of several remedies under the same section. The court can also direct that the deposition not be taken at all, that it proceed only at a different place than noticed, that it be limited to written interrogatories, that certain matters not be inquired into, that the transcript be sealed until the court orders it opened, or that trade secrets and similar information need not be disclosed. A motion can combine more than one of these where the facts justify it.
The standard the court applies
None of these orders issue automatically; good cause has to be shown, and the rule frames the whole list around a single purpose: the court may make any other order which justice requires to protect the party or witness from annoyance, embarrassment, or oppression. That is the standard your motion needs to satisfy, whether you are asking to exclude outsiders specifically or seeking some other limit on how the deposition is conducted. Simply preferring privacy is not enough on its own; the motion should explain what harm attendance by others would actually cause you.