diff --git a/src/CUTEst.jl b/src/CUTEst.jl
index 6c4ae43c..6316cf59 100644
--- a/src/CUTEst.jl
+++ b/src/CUTEst.jl
@@ -12,6 +12,7 @@ using JSON
 import Libdl.dlsym
 import REPL.TerminalMenus
 import Base.format_bytes
+import Base.RefValue
 import Printf.@sprintf
 import DataStructures: OrderedDict
 
diff --git a/src/julia_interface.jl b/src/julia_interface.jl
index 3d72383d..3187ca0d 100644
--- a/src/julia_interface.jl
+++ b/src/julia_interface.jl
@@ -324,10 +324,14 @@ function NLPModels.jac_nln_structure!(
 ) where {T}
   @lencheck nlp.meta.nln_nnzj rows cols
   k = 1
-  for i in findall(j -> j in nlp.meta.nln, nlp.jrows)
-    rows[k] = nlp.jrows[i] - count(x < nlp.jrows[i] for x in nlp.meta.lin)
-    cols[k] = nlp.jcols[i]
-    k += 1
+  for index in eachindex(nlp.jrows)
+    jr = nlp.jrows[index]
+    if jr in nlp.meta.nln
+      offset = count(x < nlp.jrows[index] for x in nlp.meta.lin)
+      rows[k] = jr - offset
+      cols[k] = nlp.jcols[index]
+      k += 1
+    end
   end
   return rows, cols
 end
@@ -759,7 +763,6 @@ function NLPModels.jth_hess_coord!(
   @rangecheck 1 nlp.meta.ncon j
   ref_j = nlp.index
   ref_j[] = j
-  nnzh_output = Ref{Cint}()
   cish(
     T,
     nlp.libsif,
@@ -767,7 +770,7 @@ function NLPModels.jth_hess_coord!(
     nlp.nvar,
     x,
     ref_j,
-    nnzh_output,
+    nlp.nnzh_jth,
     nlp.nnzh,
     vals,
     nlp.hcols,
diff --git a/src/model.jl b/src/model.jl
index 87f14265..e5eb6c2a 100644
--- a/src/model.jl
+++ b/src/model.jl
@@ -19,14 +19,15 @@ mutable struct CUTEstModel{T} <: AbstractNLPModel{T, Vector{T}}
   Jvar::Vector{Cint}
 
   libsif::Ptr{Cvoid}
-  funit::Ref{Cint}
-  index::Ref{Cint}
-  nvar::Ref{Cint}
-  ncon::Ref{Cint}
-  nnzj::Ref{Cint}
-  nnzh::Ref{Cint}
-  f::Ref{T}
-  status::Ref{Cint}
+  funit::RefValue{Cint}
+  index::RefValue{Cint}
+  nvar::RefValue{Cint}
+  ncon::RefValue{Cint}
+  nnzj::RefValue{Cint}
+  nnzh::RefValue{Cint}
+  nnzh_jth::RefValue{Cint}
+  f::RefValue{T}
+  status::RefValue{Cint}
 end
 
 """
@@ -326,6 +327,7 @@ function CUTEstModel{T}(
     Ref{Cint}(ncon),
     Ref{Cint}(nnzj),
     Ref{Cint}(nnzh),
+    Ref{Cint}(),
     Ref{T}(),
     status,
   )
diff --git a/test/runtests.jl b/test/runtests.jl
index cf0d65ef..0442c602 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -60,6 +60,7 @@ include("test_core.jl")
 include("test_julia.jl")
 include("coverage.jl")
 include("multiple_precision.jl")
+include("test_allocations.jl")
 
 for problem in problems
   for T in (Float32, Float64, Float128)
diff --git a/test/test_allocations.jl b/test/test_allocations.jl
new file mode 100644
index 00000000..42911f8e
--- /dev/null
+++ b/test/test_allocations.jl
@@ -0,0 +1,12 @@
+# using CUTEst, NLPModelsTest, NLPModels, Quadmath
+
+@testset "allocations -- $pb" for pb in ("BROWNDEN", "HS5", "HS6", "HS10", "HS11", "HS13", "HS14")
+    @testset "precision -- $T" for T in (Float32, Float64, Float128)
+        (T == Float128) && (Sys.ARCH == :aarch64) && Sys.islinux() && continue
+        nlp = CUTEstModel{T}(pb)
+        NLPModelsTest.test_zero_allocations(nlp; linear_api=true, exclude=[jac_op])
+        # mems = NLPModelsTest.test_allocs_nlpmodels(nlp; linear_api=true, exclude=[jac_op])
+        # display(mems)
+        finalize(nlp)
+    end
+end