Flight Crew Air Transport Pilot (ATP)
Communication Breakdown; Confusion
ATC Issue All Types; Deviation - Altitude Crossing Restriction Not Met; Deviation - Altitude Undershoot; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Provided Assistance; Flight Crew Became Reoriented
Airspace Structure; Human Factors
On the WAPPL4 arrival; we were told to stay at FL290 because of traffic below us; approximately at WAPPL we were told to descend via the WAPPL4; we began our descent and were fairly quickly told to descend via the WAPPL4 except maintain 7;000 at 'HUDZY.' It was a steep descent at that point but we were able to accomplish it. As we leveled at 7;000 at HUDZY we were told that we were supposed to descend via the WAPPL4; 7;000 at 'BUGZY.'HUDZY and BUGZY are too similar sounding and may need to be changed. Since we were significantly high at WAPPL due to traffic; would have been helpful to be given a simple clear altitude restriction for the next fix; like cross WLMOR at FL210 or HUDZY at FL180. It is difficult to configure the airplane for a descend via when you begin too high; then since everything was out of wack we did not think to question the altitude restriction of 7;000 at HUDZY. We should have questioned that restriction since it created a very steep descent rate.
Small Transport Captain reported similar sounding waypoint/intersection names HUDZY and BUGZY contributed to a track deviation.