diff --git a/src/Bridges/bridgeoptimizer.jl b/src/Bridges/bridgeoptimizer.jl
index 95dcc57627..ca7b9290b0 100644
--- a/src/Bridges/bridgeoptimizer.jl
+++ b/src/Bridges/bridgeoptimizer.jl
@@ -323,6 +323,25 @@ function MOI.add_constraint(b::AbstractBridgeOptimizer, f::MOI.AbstractFunction,
         return MOI.add_constraint(b.model, f, s)
     end
 end
+function MOI.add_constraints(b::AbstractBridgeOptimizer, f::Vector{F},
+                             s::Vector{S}) where { F <: MOI.AbstractFunction,
+                             S <: MOI.AbstractSet}
+    if is_bridged(b, F, S)
+        # See add_constraint for why we we call `concrete_bridge_type` separately
+        # before `add_constraints`
+        BridgeType = concrete_bridge_type(b, F, S)
+        # `add_constraints` might throw an `UnsupportedConstraint` but no
+        #  modification has been done in the previous line
+        cis = MOI.add_constraints(b.bridged, f, s)
+        for (n, ci) in enumerate(cis)
+            @assert !haskey(b.bridges, ci)
+            b.bridges[ci] = BridgeType(b, f[n], s[n])
+        end
+        return cis
+    else
+        return MOI.add_constraints(b.model, f, s)
+    end
+end
 function MOI.modify(b::AbstractBridgeOptimizer, ci::CI,
                      change::MOI.AbstractFunctionModification)
     if is_bridged(b, typeof(ci))
@@ -343,4 +362,4 @@ end
 MOI.add_variable(b::AbstractBridgeOptimizer) = MOI.add_variable(b.model)
 MOI.add_variables(b::AbstractBridgeOptimizer, n) = MOI.add_variables(b.model, n)
 
-# TODO add transform
\ No newline at end of file
+# TODO add transform
diff --git a/src/Utilities/copy.jl b/src/Utilities/copy.jl
index 98407c136d..d83dcd682a 100644
--- a/src/Utilities/copy.jl
+++ b/src/Utilities/copy.jl
@@ -151,14 +151,13 @@ Copy the constraints of type `F`-in-`S` from the model `src` the model `dest` an
 function copyconstraints!(dest::MOI.ModelLike, src::MOI.ModelLike, copy_names::Bool, idxmap::IndexMap, ::Type{F}, ::Type{S}) where {F<:MOI.AbstractFunction, S<:MOI.AbstractSet}
     # Copy constraints
     cis_src = MOI.get(src, MOI.ListOfConstraintIndices{F, S}())
-    for ci_src in cis_src
-        f_src = MOI.get(src, MOI.ConstraintFunction(), ci_src)
-        f_dest = mapvariables(idxmap, f_src)
-        s = MOI.get(src, MOI.ConstraintSet(), ci_src)
-        ci_dest = MOI.add_constraint(dest, f_dest, s)
+    f_src = MOI.get(src, MOI.ConstraintFunction(), cis_src)
+    f_dest = mapvariables.(Ref(idxmap), f_src)
+    s = MOI.get(src, MOI.ConstraintSet(), cis_src)
+    cis_dest = MOI.add_constraints(dest, f_dest, s)
+    for (ci_src, ci_dest) in zip(cis_src, cis_dest)
         idxmap.conmap[ci_src] = ci_dest
     end
-
     pass_attributes(dest, src, copy_names, idxmap, cis_src)
 end
 
@@ -184,8 +183,9 @@ function default_copy_to(dest::MOI.ModelLike, src::MOI.ModelLike, copy_names::Bo
 
     # Copy variables
     vis_src = MOI.get(src, MOI.ListOfVariableIndices())
-    for vi in vis_src
-        idxmap.varmap[vi] = MOI.add_variable(dest)
+    vars = MOI.add_variables(dest, length(vis_src))
+    for (vi, var) in zip(vis_src, vars)
+        idxmap.varmap[vi] = var
     end
 
     # Copy variable attributes