diff --git a/src/MathOptLazy.jl b/src/MathOptLazy.jl
index 331dba1..5793037 100644
--- a/src/MathOptLazy.jl
+++ b/src/MathOptLazy.jl
@@ -75,6 +75,10 @@ struct _LazyData{F<:MOI.AbstractScalarFunction,S<:MOI.AbstractScalarSet}
     end
 end
 
+Base.length(x::_LazyData) = length(x.data)
+
+Base.isempty(x::_LazyData) = isempty(x.data)
+
 ### Optimizer
 
 """
@@ -180,16 +184,6 @@ function MOI.supports(
     return MOI.supports(model.inner, arg, MOI.VariableIndex)
 end
 
-function MOI.set(
-    model::Optimizer,
-    attr::MOI.AbstractVariableAttribute,
-    indices::Vector{<:MOI.VariableIndex},
-    args::Vector{T},
-) where {T}
-    MOI.set.(model, attr, indices, args)
-    return
-end
-
 ### AbstractConstraintAttribute
 
 function MOI.is_valid(model::Optimizer, ci::MOI.ConstraintIndex)
@@ -206,10 +200,10 @@ end
 
 function MOI.set(
     model::Optimizer,
-    attr::MOI.AbstractConstraintAttribute,
-    indices::Vector{<:MOI.ConstraintIndex},
-    args::Vector{T},
-) where {T}
+    attr::Union{MOI.AbstractConstraintAttribute,MOI.AbstractVariableAttribute},
+    indices::Vector,
+    args::Vector,
+)
     MOI.set.(model, attr, indices, args)
     return
 end
@@ -286,7 +280,22 @@ function MOI.is_valid(
     ci::MOI.ConstraintIndex{F,LazyScalarSet{S}},
 ) where {F,S}
     data = _data(model, F, S)
-    return data !== nothing && 1 <= ci.value <= length(data.data)
+    return data !== nothing && 1 <= ci.value <= length(data)
+end
+
+function MOI.get(
+    model::Optimizer,
+    ::MOI.ListOfConstraintIndices{F,LazyScalarSet{S}},
+) where {F<:MOI.AbstractScalarFunction,S<:MOI.AbstractScalarSet}
+    n = length(_data(model, F, S))
+    return [MOI.ConstraintIndex{F,LazyScalarSet{S}}(i) for i in 1:n]
+end
+
+function MOI.get(
+    model::Optimizer,
+    ::MOI.NumberOfConstraints{F,LazyScalarSet{S}},
+) where {F<:MOI.AbstractScalarFunction,S<:MOI.AbstractScalarSet}
+    return length(_data(model, F, S))
 end
 
 function MOI.add_constraint(
@@ -298,25 +307,103 @@ function MOI.add_constraint(
     push!(data.data, (f, s.set))
     push!(data.active, false)
     push!(data.index, MOI.ConstraintIndex{F,S}(0))
-    return MOI.ConstraintIndex{F,LazyScalarSet{S}}(length(data.data))
+    return MOI.ConstraintIndex{F,LazyScalarSet{S}}(length(data))
 end
 
 function MOI.get(
     model::Optimizer,
     ::MOI.ConstraintFunction,
     ci::MOI.ConstraintIndex{F,LazyScalarSet{S}},
-) where {F,S}
+) where {F<:MOI.AbstractScalarFunction,S<:MOI.AbstractScalarSet}
     return _data(model, F, S).data[ci.value][1]
 end
 
+function MOI.get(
+    model::Optimizer,
+    ::MOI.CanonicalConstraintFunction,
+    ci::MOI.ConstraintIndex{F,LazyScalarSet{S}},
+) where {F<:MOI.AbstractScalarFunction,S<:MOI.AbstractScalarSet}
+    return MOI.Utilities.canonical(MOI.get(model, MOI.ConstraintFunction(), ci))
+end
+
 function MOI.get(
     model::Optimizer,
     ::MOI.ConstraintSet,
     ci::MOI.ConstraintIndex{F,LazyScalarSet{S}},
-) where {F,S}
+) where {F<:MOI.AbstractScalarFunction,S<:MOI.AbstractScalarSet}
     return LazyScalarSet(_data(model, F, S).data[ci.value][2])
 end
 
+function MOI.get(
+    model::Optimizer{T},
+    ::MOI.ListOfConstraintTypesPresent,
+) where {T}
+    ret = MOI.get(model.inner, MOI.ListOfConstraintTypesPresent())
+    if !isempty(model.saf_gt)
+        push!(
+            ret,
+            (MOI.ScalarAffineFunction{T}, LazyScalarSet{MOI.GreaterThan{T}}),
+        )
+    end
+    if !isempty(model.saf_lt)
+        push!(
+            ret,
+            (MOI.ScalarAffineFunction{T}, LazyScalarSet{MOI.LessThan{T}}),
+        )
+    end
+    return ret
+end
+
+function MOI.get(
+    model::Optimizer,
+    attr::MOI.NumberOfConstraints{F,S},
+) where {F<:MOI.AbstractScalarFunction,S<:MOI.AbstractScalarSet}
+    n = MOI.get(model.inner, attr)
+    if (data = _data(model, F, S)) !== nothing
+        n -= sum(data.active)
+    end
+    return n
+end
+
+function MOI.get(
+    model::Optimizer,
+    attr::MOI.ListOfConstraintIndices{F,S},
+) where {F<:MOI.AbstractScalarFunction,S<:MOI.AbstractScalarSet}
+    ret = MOI.get(model.inner, attr)
+    if (data = _data(model, F, S)) !== nothing
+        in_model = Set(ci for (ci, z) in zip(data.index, data.active) if z)
+        ret = filter!(ci -> !(ci in in_model), ret)
+    end
+    return ret
+end
+
+function MOI.supports(
+    model::Optimizer,
+    ::MOI.AbstractConstraintAttribute,
+    ::Type{MOI.ConstraintIndex{F,LazyScalarSet{S}}},
+) where {F<:MOI.AbstractScalarFunction,S<:MOI.AbstractScalarSet}
+    return false
+end
+
+function MOI.get(
+    model::Optimizer,
+    attr::MOI.AbstractConstraintAttribute,
+    ::MOI.ConstraintIndex{F,LazyScalarSet{S}},
+) where {F<:MOI.AbstractScalarFunction,S<:MOI.AbstractScalarSet}
+    msg = "This attribute is not supported for lazy constraints"
+    return throw(MOI.GetAttributeNotAllowed(attr, msg))
+end
+
+function MOI.set(
+    model::Optimizer,
+    attr::MOI.AbstractConstraintAttribute,
+    ::MOI.ConstraintIndex{F,LazyScalarSet{S}},
+    value::Any,
+) where {F<:MOI.AbstractScalarFunction,S<:MOI.AbstractScalarSet}
+    msg = "This attribute is not supported for lazy constraints"
+    return throw(MOI.SetAttributeNotAllowed(attr, msg))
+end
+
 ### MOI.optimize!
 
 function MOI.optimize!(model::Optimizer{T}) where {T}
diff --git a/test/runtests.jl b/test/runtests.jl
index c261e8e..d9e4fd8 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -33,7 +33,8 @@ function test_jump_cached_knapsack()
     model = Model(() -> MathOptLazy.Optimizer(HiGHS.Optimizer))
     set_silent(model)
     @variable(model, x[1:N] >= 0, Int)
-    @constraint(model, [i in 1:N], x[i] <= 1, MathOptLazy.Lazy())
+    @constraint(model, c[i in 1:N], x[i] <= 1, MathOptLazy.Lazy())
+    @test endswith(sprint(show, c[1]), " [lazy]")
     @constraint(model, sum(abs(cos(i)) * x[i] for i in 1:N) <= 0.1 * N)
     @objective(model, Max, sum(abs(sin(i)) * x[i] for i in 1:N))
     optimize!(model)
@@ -58,6 +59,18 @@ function test_jump_direct_knapsack()
     return
 end
 
+function test_jump_broadcast()
+    model = Model(() -> MathOptLazy.Optimizer(HiGHS.Optimizer))
+    @variable(model, x[1:3])
+    c = @constraint(model, x .<= 1:3, MathOptLazy.Lazy())
+    @test c isa Vector && length(c) == 3
+    for (i, ci) in enumerate(c)
+        @test constraint_object(ci).set ==
+              MathOptLazy.LazyScalarSet(MOI.LessThan{Float64}(i))
+    end
+    return
+end
+
 function test_jump_direct_basics()
     model = direct_model(MathOptLazy.Optimizer(HiGHS.Optimizer))
     @variable(model, x)
@@ -68,6 +81,87 @@ function test_jump_direct_basics()
     return
 end
 
+function _basic_constraint_test_helper(
+    function_fn::Function,
+    inner_set::MOI.AbstractScalarSet;
+    activate::Bool,
+)
+    model = MathOptLazy.Optimizer(HiGHS.Optimizer)
+    config = MOI.Test.Config()
+    set = MathOptLazy.LazyScalarSet(inner_set)
+    N = MOI.dimension(set)
+    x = MOI.add_variables(model, 3)
+    constraint_function = function_fn(x)
+    @test MOI.output_dimension(constraint_function) == N
+    F, S, IS = typeof(constraint_function), typeof(set), typeof(inner_set)
+    @test MOI.supports_constraint(model, F, S)
+    @test MOI.get(model, MOI.NumberOfConstraints{F,S}()) == 0
+    c = MOI.add_constraint(model, constraint_function, set)
+    if activate
+        data = MathOptLazy._data(model, F, IS)
+        for (i, (f, s)) in enumerate(data.data)
+            data.index[i] = MOI.add_constraint(model.inner, f, s)
+            data.active[i] = true
+        end
+    end
+    c_inner = MOI.add_constraint(model, constraint_function, inner_set)
+    @test MOI.get(model, MOI.NumberOfConstraints{F,S}()) == 1
+    @test MOI.get(model, MOI.NumberOfConstraints{F,IS}()) == 1
+    @test MOI.get(model, MOI.ListOfConstraintIndices{F,S}()) == [c]
+    @test MOI.get(model, MOI.ListOfConstraintIndices{F,IS}()) == [c_inner]
+    @test (F, S) in MOI.get(model, MOI.ListOfConstraintTypesPresent())
+    @test MOI.is_valid(model, c)
+    @test !MOI.is_valid(model, typeof(c)(c.value + 1)) isa Bool
+    @test !MOI.is_valid(model, typeof(c)(c.value - 1)) isa Bool
+    @test !MOI.is_valid(model, typeof(c)(c.value + 12345))
+    # Don't compare directly, because `f` might not be canonicalized.
+    f = MOI.get(model, MOI.ConstraintFunction(), c)
+    @test isapprox(f, constraint_function, config)
+    cf = MOI.get(model, MOI.CanonicalConstraintFunction(), c)
+    @test isapprox(cf, constraint_function, config)
+    @test MOI.get(model, MOI.ConstraintSet(), c) == set
+    MOI.add_constraints(
+        model,
+        [constraint_function, constraint_function],
+        [set, set],
+    )
+    @test MOI.get(model, MOI.NumberOfConstraints{F,S}()) == 3
+    @test length(MOI.get(model, MOI.ListOfConstraintIndices{F,S}())) == 3
+    c_indices = MOI.get(model, MOI.ListOfConstraintIndices{F,S}())
+    @test all(MOI.is_valid.(model, c_indices))
+    MOI.set(model, MOI.ConstraintName(), [c_inner], ["c"])
+    @test MOI.get(model, MOI.ConstraintName(), [c_inner]) == ["c"]
+    @test_throws(
+        MOI.SetAttributeNotAllowed,
+        MOI.set(model, MOI.ConstraintName(), [c], ["c"]),
+    )
+    @test_throws(
+        MOI.GetAttributeNotAllowed,
+        MOI.get(model, MOI.ConstraintName(), [c]),
+    )
+    return
+end
+
+function test_basic_scalaraffinefunction_greaterthan()
+    _basic_constraint_test_helper(MOI.GreaterThan(1.0); activate = true) do x
+        return sum(sin(i) * x[i] for i in 1:length(x))
+    end
+    _basic_constraint_test_helper(MOI.GreaterThan(1.0); activate = false) do x
+        return sum(sin(i) * x[i] for i in 1:length(x))
+    end
+    return
+end
+
+function test_basic_scalaraffinefunction_lessthan()
+    _basic_constraint_test_helper(MOI.LessThan(1.0); activate = true) do x
+        return sum(sin(i) * x[i] for i in 1:length(x))
+    end
+    _basic_constraint_test_helper(MOI.LessThan(1.0); activate = false) do x
+        return sum(sin(i) * x[i] for i in 1:length(x))
+    end
+    return
+end
+
 end  # TestMathOptLazy
 
 TestMathOptLazy.runtests()