All City Letter Carriers and Assistants have a contract with the USPS. Every letter carrier has negotiated their contract through the Union of all letter carriers, the NALC. The NALC bargains for everything regarding wages, hours, and working conditions, and enforces those items in the contract. Article 19 of the contract covers handbooks and manuals the USPS produces whenever they have anything to do with wages, hours, or working conditions.

From the JCAM (Joint Contract Administration Manual):

Handbooks and Manuals. Article 19 provides that those postal handbook and manual provisions directly relating to wages, hours, or working conditions are enforceable as though they were part of the National Agreement.

So the M-41 Handbook, City Delivery Carriers Duties and Responsibilities, is part of our National Contract.

Page 1 of the M-41:

 General Information
11 Responsibilities of Carrier
111 Scope of Responsibilities
Every carrier is responsible for the items listed under part 112. However, the carrier’s responsibilities are not limited to those specific items.
112 General Responsibilities
112.1 Efficient Service
Provide reliable and efficient service. Federal statutes provide penalties for persons who knowingly or willfully obstruct or retard the mail. The statutes do not afford employees immunity from arrest for violations of law.
112.2 Diligence and Promptness
112.21 Obey the instructions of your manager.
112.22 Report for work promptly as scheduled.
112.23 Complete time records to accurately reflect the hours employed each day.
112.24 Display a willing attitude and put forth a conscientious effort in developing skills to perform duties assigned.
112.25 Be prompt, courteous, and obliging in the performance of duties. Attend quietly and diligently to work and refrain from loud talking and the use of profane language.
112.26 Do not report at cases or racks before tour of duty is scheduled to begin or linger about cases or racks after tour has ended.
112.27 Do not move mail from place to place on or adjacent to your case. Do not engage in any time wasting practices before placing mail in the proper separation.
112.28 Do not loiter or stop to converse unnecessarily on your route.
112.29 Return to the delivery unit immediately on completion of assigned street duties and promptly clock in on arrival. A motorized carrier unloads his vehicle and then immediately records returning time.

So, there, in a nice one page read is a basic introduction to the city letter carrier job. 

Notice the lack of any language which indicates being speedy, quick, or fast. Instead the professional letter carrier is diligent. A dictionary definition: