Large language models (LLMs) are now widely used to draft and refactor code, but code that works is not necessarily secure. We evaluate secure code generation using the Instruct Prime, which eliminated compliance-required prompts and cue contamination, and evaluate five instruction-tuned code LLMs using a zero-shot baseline and a three-round reflexion prompting approach. Security is measured using the Insecure Code Detector (ICD), and results are reported by measuring Repair, Regression, and NetGain metrics, considering the programming language and CWE family. Our findings show that insecurity remains common at the first round: roughly 25-33% of programs are insecure at a zero-shot baseline (t0 ). Weak cryptography/config-dependent bugs are the hardest to avoid while templated ones like XSS, code injection, and hard-coded secrets are handled more reliably. Python yields the highest secure rates; C and C# are the lowest, with Java, JS, PHP, and C++ in the middle. Reflexion prompting improves security for all models, improving average accuracy from 70.74% at t0 to 79.43% at t3 , with the largest gains in the first round followed by diminishing returns. The trends with Repair, Regression, and NetGain metrics show that applying one to two rounds produces most of the benefits. A replication package is available at https://doi.org/10.5281/zenodo.17065846.