I share Your disappointment about those titles. They are highly recommended, but contain not so few examples of bad practices. Long and complicated methods, mixing abstraction levels in a single function... This style certainly doesn't strive for code reuse. Readability also suffers. Lots of other complaints...
Maybe they are not focused completely and only at the core, but here are few of the best I read so far:
Sun's Certified Java Programmer for Java 6: This book can be a real eye opener even for seasoned Java developers. This I'd recommend the most since it covers a lot basic and intermediate topics written by people with a lot of technical discipline.
Effective Java: Written by the author of Java Collection Framework gives deep insight about why and how certain Java API parts work and how to make most effective use of them. Also contains few confessions about controversial parts of Java API.
Head First: Design Patterns: Nice introduction to design patterns. While it's certainly unique in style, the book approaches the topic from real-world problems.
Practical API design: We, as programmers, always produce code which is used by others. This book focuses on how to make using of your code or library as plausible as possible. If you're not writing only for yourself that really matters.
Clean Code: "Even bad code can function. But if code isn’t clean, it can bring a development organization to its knees. Every year, countless hours and significant resources are lost because of poorly written code. But it doesn’t have to be that way"
Java Concurrency in Practice: It's certainly not core, but a great one. It tackles concurrent programming. Processor clock rates aren't rising so quickly as before. Some say that the multi-core processors can extend Moore's Law in future years, so it's good to know how to use them. Especially worth noting are articles on IBM tech library written by the same author.
Disclaimer: They aren't strictly Core Java alternatives. While I learned the essentials of Java I faced a certain point I got stuck in. At the other hand books I recommend gave back the wind in my sails. And quite astonishingly, gave me a much better understanding about Core Java than books which advertise that in title.