diff --git a/src/JuMP_wrapper.jl b/src/JuMP_wrapper.jl
index 73d5d2f..331b860 100644
--- a/src/JuMP_wrapper.jl
+++ b/src/JuMP_wrapper.jl
@@ -15,7 +15,7 @@ include("operators.jl")
     end
 
 Iterator `iterators[index.value]`.
-""" # TODO remove
+"""
 struct IteratorInExpr
     iterators::Iterators
     index::IteratorIndex
diff --git a/src/operators.jl b/src/operators.jl
index 1fd2308..447b444 100644
--- a/src/operators.jl
+++ b/src/operators.jl
@@ -254,6 +254,12 @@ end
 
 JuMP._is_real(::LazySum) = true
 JuMP.variable_ref_type(s::LazySum) = JuMP.variable_ref_type(s.expr)
+
+# `JuMP.:+(::AbstractJuMPScalar, ::AbstractJuMPScalar)` calls `iszero` which
+# defaults to `x == zero(x)`. A `LazySum` is never simplified away so we
+# short-circuit it here, this avoids needing `zero(::Type{<:LazySum})`.
+Base.iszero(::LazySum) = false
+
 function JuMP.check_belongs_to_model(s::LazySum, model::JuMP.AbstractModel)
     return JuMP.check_belongs_to_model(s.expr, model)
 end
diff --git a/test/operators.jl b/test/operators.jl
index 001d2d4..8dd55c2 100644
--- a/test/operators.jl
+++ b/test/operators.jl
@@ -8,6 +8,7 @@ module TestOperators
 using Test
 using GenOpt
 import JuMP
+import MathOptInterface as MOI
 
 function runtests()
     for name in names(@__MODULE__; all = true)
@@ -65,6 +66,23 @@ function test_multivariate()
     @test ijxx isa GenOpt.ExprTemplate{JuMP.QuadExpr,JuMP.VariableRef}
 end
 
+function test_lazy_sum_sum()
+    model = JuMP.Model()
+    JuMP.@variable(model, x[1:2])
+    a = lazy_sum(x[i]^2 for i in 1:2)
+    b = lazy_sum(2 * x[i] for i in 1:2)
+    @test a isa GenOpt.LazySum{JuMP.QuadExpr,JuMP.VariableRef}
+    @test b isa GenOpt.LazySum{JuMP.AffExpr,JuMP.VariableRef}
+    JuMP.@objective(model, Min, a + b)
+    F = MOI.get(model, MOI.ObjectiveFunctionType())
+    @test F == MOI.ScalarNonlinearFunction
+    func = MOI.get(model, MOI.ObjectiveFunction{F}())
+    @test func.head == :+
+    @test func.args[1] isa SumGenerator{MOI.ScalarQuadraticFunction{Float64}}
+    @test func.args[2] isa SumGenerator{MOI.ScalarAffineFunction{Float64}}
+    return
+end
+
 end  # module
 
 TestOperators.runtests()