diff --git a/make/program b/make/program
index 6aa40348e1..16f2818be5 100644
--- a/make/program
+++ b/make/program
@@ -16,19 +16,20 @@ $(CMDSTAN_MAIN_O) : $(CMDSTAN_MAIN)
 ##
 # Precompiled model header
 ##
-$(STAN)src/stan/model/model_header$(STAN_FLAGS)_$(CXX_MAJOR)_$(CXX_MINOR).d : $(STAN)src/stan/model/model_header.hpp
+$(patsub %.d,%.hpp.gch,$(PRECOMPILED_MODEL_HEADER)) : $(STAN)src/stan/model/model_header.hpp
 	$(COMPILE.cpp) $(DEPFLAGS) $<
 
 ifneq ($(PRECOMPILED_MODEL_HEADER),)
-$(STAN)src/stan/model/model_header$(STAN_FLAGS)_$(CXX_MAJOR)_$(CXX_MINOR).d : DEPTARGETS = -MT $(patsubst %.d,%.hpp.gch,$@) -MT $@
-$(STAN)src/stan/model/model_header$(STAN_FLAGS)_$(CXX_MAJOR)_$(CXX_MINOR).hpp.gch : $(STAN)src/stan/model/model_header.hpp
+$(patsub %.d,%.hpp.gch,$(PRECOMPILED_MODEL_HEADER)) : DEPTARGETS = -MT $(patsubst %.d,%.hpp.gch,$@) -MT $@
+$(PRECOMPILED_MODEL_HEADER) : $(STAN)src/stan/model/model_header.hpp
 	@echo ''
 	@echo '--- Compiling pre-compiled header. This might take a few seconds. ---'
+	@mkdir $(dir $@)
 	$(COMPILE.cpp) $< $(OUTPUT_OPTION)
 
 ifeq ($(CXX_TYPE),clang)
-CXXFLAGS_PROGRAM += -include-pch $(STAN)src/stan/model/model_header$(STAN_FLAGS)_$(CXX_MAJOR)_$(CXX_MINOR).hpp.gch
-$(STAN_TARGETS) : %$(EXE) : $(STAN)src/stan/model/model_header$(STAN_FLAGS)_$(CXX_MAJOR)_$(CXX_MINOR).hpp.gch
+CXXFLAGS_PROGRAM += -include-pch $(PRECOMPILED_MODEL_HEADER)
+$(STAN_TARGETS) : %$(EXE) : $(PRECOMPILED_MODEL_HEADER)
 endif
 endif
 
diff --git a/makefile b/makefile
index 2fe8e82524..2ccd2eeab9 100644
--- a/makefile
+++ b/makefile
@@ -132,7 +132,7 @@ PRECOMPILED_HEADERS ?= true
 endif
 
 ifeq ($(PRECOMPILED_HEADERS),true)
-PRECOMPILED_MODEL_HEADER=$(STAN)src/stan/model/model_header$(STAN_FLAGS)_$(CXX_MAJOR)_$(CXX_MINOR).hpp.gch
+PRECOMPILED_MODEL_HEADER=$(STAN)src/stan/model/model_header.hpp.gch/model_header$(STAN_FLAGS)_$(CXX_MAJOR)_$(CXX_MINOR).hpp.gch
 ifeq ($(CXX_TYPE),gcc)
 CXXFLAGS_PROGRAM+= -Wno-ignored-attributes $(CXXFLAGS_OPTIM) $(CXXFLAGS_FLTO)
 endif
@@ -284,6 +284,7 @@ clean: clean-tests
 	$(RM) -r bin/cmdstan
 	@echo '  removing cached compiler objects'
 	$(RM) $(wildcard src/cmdstan/main*.o) $(wildcard $(STAN)src/stan/model/model_header*.hpp.gch)
+	$(RM) -r $(STAN)src/stan/model/model_header.hpp.gch/
 	@echo '  removing built example model'
 	$(RM) examples/bernoulli/bernoulli$(EXE) examples/bernoulli/bernoulli.o examples/bernoulli/bernoulli.d examples/bernoulli/bernoulli.hpp $(wildcard examples/bernoulli/*.csv)