diff --git a/src/Bridges/Constraint/Constraint.jl b/src/Bridges/Constraint/Constraint.jl
index 734bbbb07b..8b67cf9904 100644
--- a/src/Bridges/Constraint/Constraint.jl
+++ b/src/Bridges/Constraint/Constraint.jl
@@ -22,97 +22,115 @@ for filename in readdir(joinpath(@__DIR__, "bridges"); join = true)
 end
 
 """
-    add_all_bridges(bridged_model, ::Type{T}) where {T}
+    add_all_bridges(model, ::Type{T}) where {T}
 
-Add all bridges defined in the `Bridges.Constraint` submodule to
-`bridged_model`. The coefficient type used is `T`.
-"""
-function add_all_bridges(bridged_model, ::Type{T}) where {T}
-    if T <: AbstractFloat
-        MOI.Bridges.add_bridge(bridged_model, GreaterToIntervalBridge{T})
-        MOI.Bridges.add_bridge(bridged_model, LessToIntervalBridge{T})
-    end
-    MOI.Bridges.add_bridge(bridged_model, GreaterToLessBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, LessToGreaterBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, NonnegToNonposBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, NonposToNonnegBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, ScalarizeBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, VectorizeBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, ScalarSlackBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, VectorSlackBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, ScalarFunctionizeBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, VectorFunctionizeBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, ToScalarQuadraticBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, ToVectorQuadraticBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, ToScalarNonlinearBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, SplitHyperRectangleBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, SplitIntervalBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, SplitComplexEqualToBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, SplitComplexZerosBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, QuadtoSOCBridge{T})
-    # We do not add `(R)SOCtoNonConvexQuad` because it starts with a convex
-    # conic constraint and generate a non-convex constraint (in the QCP
-    # interpretation).
-    MOI.Bridges.add_bridge(bridged_model, NormInfinityBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, NormOneBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, GeoMeantoRelEntrBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, GeoMeanBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, GeoMeanToPowerBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, NormToPowerBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, NormOneConeToNormConeBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, SecondOrderConeToNormConeBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, NormInfinityConeToNormConeBridge{T})
-    MOI.Bridges.add_bridge(
-        bridged_model,
-        ComplexNormInfinityToSecondOrderConeBridge{T},
-    )
-    MOI.Bridges.add_bridge(bridged_model, RelativeEntropyBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, NormSpectralBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, NormNuclearBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, HermitianToSymmetricPSDBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, SquareBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, SetDotScalingBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, SetDotInverseScalingBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, LogDetBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, RootDetBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, RSOCtoSOCBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, SOCtoRSOCBridge{T})
-    # We do not add `SOCtoPSDBridge` as transforming the `SOC` to `RSOC` and
-    # then to `PSD` produces a smaller SDP constraint.
-    # MOI.Bridges.add_bridge(bridged_model, SOCtoPSDBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, RSOCtoPSDBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, IndicatorActiveOnFalseBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, IndicatorSOS1Bridge{T})
-    MOI.Bridges.add_bridge(bridged_model, IndicatorLessToGreaterThanBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, IndicatorGreaterToLessThanBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, SemiToBinaryBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, ZeroOneBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, IntegerToZeroOneBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, InequalityToComplementsBridge{T})
-    # Do not add by default
-    # MOI.Bridges.add_bridge(bridged_model, NumberConversionBridge{T})
-    # Constraint programming bridges
-    MOI.Bridges.add_bridge(bridged_model, AllDifferentToCountDistinctBridge{T})
-    MOI.Bridges.add_bridge(
-        bridged_model,
-        ReifiedAllDifferentToCountDistinctBridge{T},
-    )
-    MOI.Bridges.add_bridge(bridged_model, BinPackingToMILPBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, CircuitToMILPBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, CountAtLeastToCountBelongsBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, CountBelongsToMILPBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, CountDistinctToMILPBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, ReifiedCountDistinctToMILPBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, CountGreaterThanToMILPBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, TableToMILPBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, SOS1ToMILPBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, SOS2ToMILPBridge{T})
-    MOI.Bridges.add_bridge(bridged_model, IndicatorToMILPBridge{T})
+Add all bridges defined in the `Bridges.Constraint` submodule to `model`.
 
+The coefficient type used is `T`.
+"""
+function add_all_bridges(model, ::Type{T}) where {T}
+    MOI.Bridges.add_bridge(model, AllDifferentToCountDistinctBridge{T})
+    MOI.Bridges.add_bridge(model, BinPackingToMILPBridge{T})
+    MOI.Bridges.add_bridge(model, CircuitToMILPBridge{T})
+    MOI.Bridges.add_bridge(model, ComplexNormInfinityToSecondOrderConeBridge{T})
+    MOI.Bridges.add_bridge(model, CountAtLeastToCountBelongsBridge{T})
+    MOI.Bridges.add_bridge(model, CountBelongsToMILPBridge{T})
+    MOI.Bridges.add_bridge(model, CountDistinctToMILPBridge{T})
+    MOI.Bridges.add_bridge(model, CountGreaterThanToMILPBridge{T})
     MOI.Bridges.add_bridge(
-        bridged_model,
+        model,
         ExponentialConeToScalarNonlinearFunctionBridge{T},
     )
+    #  * FunctionConversionBridge{T}
+    #      This bridge is not added because, even though it is not abstract, it
+    #      is highly parameterized, and parameterized versions such as
+    #      ScalarFunctionizeBridge are added.
+    MOI.Bridges.add_bridge(model, GeoMeanBridge{T})
+    MOI.Bridges.add_bridge(model, GeoMeanToPowerBridge{T})
+    MOI.Bridges.add_bridge(model, GeoMeantoRelEntrBridge{T})
+    if T <: AbstractFloat
+        MOI.Bridges.add_bridge(model, GreaterToIntervalBridge{T})
+    end
+    MOI.Bridges.add_bridge(model, GreaterToLessBridge{T})
+    MOI.Bridges.add_bridge(model, HermitianToSymmetricPSDBridge{T})
+    MOI.Bridges.add_bridge(model, IndicatorActiveOnFalseBridge{T})
+    MOI.Bridges.add_bridge(model, IndicatorGreaterToLessThanBridge{T})
+    MOI.Bridges.add_bridge(model, IndicatorLessToGreaterThanBridge{T})
+    #  * IndicatorSetMapBridge{T}
+    #      This bridge is not added because, even though it is not abstract, it
+    #      is highly parameterized, and parameterized versions such as
+    #      IndicatorGreaterToLessThanBridge are added.
+    MOI.Bridges.add_bridge(model, IndicatorSOS1Bridge{T})
+    MOI.Bridges.add_bridge(model, IndicatorToMILPBridge{T})
+    MOI.Bridges.add_bridge(model, InequalityToComplementsBridge{T})
+    MOI.Bridges.add_bridge(model, IntegerToZeroOneBridge{T})
+    MOI.Bridges.add_bridge(model, LessToGreaterBridge{T})
+    if T <: AbstractFloat
+        MOI.Bridges.add_bridge(model, LessToIntervalBridge{T})
+    end
+    MOI.Bridges.add_bridge(model, LogDetBridge{T})
+    MOI.Bridges.add_bridge(model, NonnegToNonposBridge{T})
+    MOI.Bridges.add_bridge(model, NonposToNonnegBridge{T})
+    MOI.Bridges.add_bridge(model, NormInfinityBridge{T})
+    MOI.Bridges.add_bridge(model, NormInfinityConeToNormConeBridge{T})
+    MOI.Bridges.add_bridge(model, NormNuclearBridge{T})
+    MOI.Bridges.add_bridge(model, NormOneBridge{T})
+    MOI.Bridges.add_bridge(model, NormOneConeToNormConeBridge{T})
+    #  * NormSpecialCaseBridge{T}
+    #      This bridge is not added because, even though it is not abstract, it
+    #      is highly parameterized, and parameterized versions such as
+    #      NormOneConeToNormConeBridge are added.
+    MOI.Bridges.add_bridge(model, NormSpectralBridge{T})
+    MOI.Bridges.add_bridge(model, NormToPowerBridge{T})
+    #  * NumberConversionBridge{T}
+    #      This bridge is not added by default because it would silently enable
+    #      models with mixed precision. In most cases, this is a bug in the
+    #      user's code, so we leave this bridge as opt-in.
+    MOI.Bridges.add_bridge(model, QuadtoSOCBridge{T})
+    MOI.Bridges.add_bridge(model, ReifiedAllDifferentToCountDistinctBridge{T})
+    MOI.Bridges.add_bridge(model, ReifiedCountDistinctToMILPBridge{T})
+    MOI.Bridges.add_bridge(model, RelativeEntropyBridge{T})
+    MOI.Bridges.add_bridge(model, RootDetBridge{T})
+    #  * RSOCtoNonConvexQuadBridge{T}
+    #      This bridge is not added by default because it starts with a convex
+    #      conic constraint and generate a non-convex constraint (in the QCP
+    #      interpretation).
+    MOI.Bridges.add_bridge(model, RSOCtoPSDBridge{T})
+    MOI.Bridges.add_bridge(model, RSOCtoSOCBridge{T})
+    MOI.Bridges.add_bridge(model, ScalarFunctionizeBridge{T})
+    MOI.Bridges.add_bridge(model, ScalarizeBridge{T})
+    MOI.Bridges.add_bridge(model, ScalarSlackBridge{T})
+    MOI.Bridges.add_bridge(model, SecondOrderConeToNormConeBridge{T})
+    MOI.Bridges.add_bridge(model, SemiToBinaryBridge{T})
+    #  * SetConversionBridge{T}
+    #      This bridge is not added because, even though it is not abstract, it
+    #      is highly parameterized, and it intended for use by MOI extensions.
+    MOI.Bridges.add_bridge(model, SetDotInverseScalingBridge{T})
+    MOI.Bridges.add_bridge(model, SetDotScalingBridge{T})
+    #  * SOCtoNonConvexQuadBridge{T}
+    #      This bridge is not added by default because it starts with a convex
+    #      conic constraint and generate a non-convex constraint (in the QCP
+    #      interpretation).
+    #  * SOCtoPSDBridge{T}
+    #      This bridge is not added because transforming the `SOC` to `RSOC` and
+    #      then to `PSD` produces a smaller SDP constraint. `RSOCtoPSDBridge` is
+    #      added by default.
+    MOI.Bridges.add_bridge(model, SOCtoRSOCBridge{T})
+    MOI.Bridges.add_bridge(model, SOS1ToMILPBridge{T})
+    MOI.Bridges.add_bridge(model, SOS2ToMILPBridge{T})
+    MOI.Bridges.add_bridge(model, SplitComplexEqualToBridge{T})
+    MOI.Bridges.add_bridge(model, SplitComplexZerosBridge{T})
+    MOI.Bridges.add_bridge(model, SplitHyperRectangleBridge{T})
+    MOI.Bridges.add_bridge(model, SplitIntervalBridge{T})
+    MOI.Bridges.add_bridge(model, SquareBridge{T})
+    MOI.Bridges.add_bridge(model, TableToMILPBridge{T})
+    MOI.Bridges.add_bridge(model, ToScalarNonlinearBridge{T})
+    MOI.Bridges.add_bridge(model, ToScalarQuadraticBridge{T})
+    MOI.Bridges.add_bridge(model, ToVectorQuadraticBridge{T})
+    MOI.Bridges.add_bridge(model, VectorFunctionizeBridge{T})
+    MOI.Bridges.add_bridge(model, VectorizeBridge{T})
+    MOI.Bridges.add_bridge(model, VectorSlackBridge{T})
+    MOI.Bridges.add_bridge(model, ZeroOneBridge{T})
     return
 end
 
diff --git a/src/Bridges/Variable/Variable.jl b/src/Bridges/Variable/Variable.jl
index 1cffd8fd62..d15633e9f9 100644
--- a/src/Bridges/Variable/Variable.jl
+++ b/src/Bridges/Variable/Variable.jl
@@ -25,15 +25,15 @@ Add all bridges defined in the `Bridges.Variable` submodule to `model`.
 The coefficient type used is `T`.
 """
 function add_all_bridges(model, ::Type{T}) where {T}
-    MOI.Bridges.add_bridge(model, ZerosBridge{T})
     MOI.Bridges.add_bridge(model, FreeBridge{T})
-    MOI.Bridges.add_bridge(model, NonposToNonnegBridge{T})
-    MOI.Bridges.add_bridge(model, VectorizeBridge{T})
-    MOI.Bridges.add_bridge(model, SOCtoRSOCBridge{T})
-    MOI.Bridges.add_bridge(model, RSOCtoSOCBridge{T})
-    MOI.Bridges.add_bridge(model, RSOCtoPSDBridge{T})
     MOI.Bridges.add_bridge(model, HermitianToSymmetricPSDBridge{T})
+    MOI.Bridges.add_bridge(model, NonposToNonnegBridge{T})
     MOI.Bridges.add_bridge(model, ParameterToEqualToBridge{T})
+    MOI.Bridges.add_bridge(model, RSOCtoPSDBridge{T})
+    MOI.Bridges.add_bridge(model, RSOCtoSOCBridge{T})
+    MOI.Bridges.add_bridge(model, SOCtoRSOCBridge{T})
+    MOI.Bridges.add_bridge(model, VectorizeBridge{T})
+    MOI.Bridges.add_bridge(model, ZerosBridge{T})
     return
 end