For network computing on desktop machines, fast execution of Java bytecode programs is essential because these machines are expected to run substantial application programs written in Java. We believe higher Java performance can be achieved by exploiting instruction-level parallelism (ILP) in the context of Java JIT compilation. This paper introduces VLaTTe, a Java JIT compiler for VLIW machines that performs efficient scheduling while doing fast register allocation. It is an extended version of our previous JIT compiler for RISC machines called LaTTe whose translation overhead is low (i.e., consistently taking one or two seconds for SPECJVM98 benchmarks) due to its fast register allocation. VLaTTe adds the scheduling capability onto the same framework of register allocation, with a constraint for precise in-order exception handling which guarantees the same Java exception behavior with the original bytecode program. Our experimental results on the SPECJVM98 benchmarks show that VLaTTe achieves a geometric mean of useful IPC 1.7 (2-ALU), 2.1 (4-ALU), and 2.3 (8-ALU), while the scheduling/allocation overhead is 3.6 times longer than LaTTe's on average, which appears to be reasonable.