Shallow-n grammars (deGispert 2010) were introduced to reduce over-generation in the Hiero translation model (Chiang 2005) resulting in much faster decoding and restricting reordering to a desired level for specific language pairs. However, Shallow-n grammars require parameters which cannot be directly optimized using minimum error-rate tuning by the decoder. This paper introduces some novel improvements to the translation model for Shallow-n grammars. We introduce two rules: a BITG-style reordering glue rule and a simpler monotonic concatenation rule. We use separate features for the new rules in our log-linear model allowing the decoder to directly optimize the feature weights. We show this formulation of Shallow-n hierarchical phrase-based translation is comparable in translation quality to full Hiero-style decoding (without shallow rules) while at the same time being considerably faster.