diff --git a/src/estimator/mhe/construct.jl b/src/estimator/mhe/construct.jl
index b22e07cfb..619ad598f 100644
--- a/src/estimator/mhe/construct.jl
+++ b/src/estimator/mhe/construct.jl
@@ -214,7 +214,13 @@ struct MovingHorizonEstimator{
         U0,  Ue  = fill(NT(NaN), nu*He),     fill(NT(NaN),  nu*(He+1))
         D0,  De  = fill(NT(NaN), nd*(He+1)), fill(NT(NaN),  nd*(He+1))
         X̂0_old   = fill(NT(NaN), nx̂*He)
-        D0[1:nd] .= 0 # D0 start with d0(-1) and it should not be NaN
+        D0[1:nd] .= 0 # D0 starts with d0(-1) and it should not be NaN
+        if direct # the following windows all start at k=-1, thus replace the NaN values:
+            Yem[1:ny] .= @views model.yop[i_ym]
+            U0[1:nu]  .= 0
+            Ue[1:nu]  .= model.uop
+            De[1:nd]  .= model.dop
+        end
         x̂0arr_old = zeros(NT, nx̂)
         P̂arr_old = copy(cov.P̂_0)
         Nk = [0]
diff --git a/test/2_test_state_estim.jl b/test/2_test_state_estim.jl
index aab23e1e6..b47ebeee8 100644
--- a/test/2_test_state_estim.jl
+++ b/test/2_test_state_estim.jl
@@ -898,6 +898,11 @@ end
     @test mhe1.nxs == 2
     @test mhe1.nx̂ == 6
     @test size(mhe1.Ẽ, 2) == 6*mhe1.nx̂
+    @test all(isfinite, mhe1.U0[1:2])
+    @test all(isnan,    mhe1.Y0m[1:2])
+    @test all(isfinite, mhe1.Yem[1:2])
+    @test all(isfinite, mhe1.D0[1:1])
+    @test all(isfinite, mhe1.De[1:1])
 
     mhe3 = MovingHorizonEstimator(linmodel, He=5, i_ym=[2])
     @test mhe3.nym == 1
@@ -960,7 +965,7 @@ end
     mhe15 = MovingHorizonEstimator(linmodel; He=1, σP_0, covestim)
     @test mhe15.cov.invP̄ ≈ inv(covestim.cov.P̂)
 
-    function gcl(X̂e, _ , _ , _ , _ , _ , _ , _ , nx, ε)
+    function gcl(X̂e, _ , _ , _ , _ , _ , _ , _ , nc, ε)
         gc = X̂e .- 100 .- ε   
         return [gc; zeros(nc .- length(X̂e))]
     end