diff --git a/src/Hamiltonians/abstract.jl b/src/Hamiltonians/abstract.jl
index e95601601..36facc2ee 100644
--- a/src/Hamiltonians/abstract.jl
+++ b/src/Hamiltonians/abstract.jl
@@ -63,7 +63,7 @@ When extending [`AbstractFockAddress`](@ref), define a method for
 dimension(h::AbstractHamiltonian) = dimension(h, starting_address(h))
 dimension(::AbstractHamiltonian, addr) = dimension(addr)
 dimension(addr::AbstractFockAddress) = dimension(typeof(addr))
-# dimension(_) = Inf # fallback
+dimension(::T) where {T<:Number} = typemax(T) # e.g. integer addresses
 
 function dimension(::Type{<:BoseFS{N,M}}) where {N,M}
     return number_conserving_bose_dimension(N,M)
diff --git a/src/Interfaces/hamiltonians.jl b/src/Interfaces/hamiltonians.jl
index be7515b83..553e179e4 100644
--- a/src/Interfaces/hamiltonians.jl
+++ b/src/Interfaces/hamiltonians.jl
@@ -18,14 +18,15 @@ For available implementations see [`Hamiltonians`](@ref Main.Hamiltonians).
 
 # Interface
 
-Methods that need to be implemented:
+Basic interface methods to implement:
 
-* [`num_offdiagonals(::AbstractHamiltonian, address)`](@ref)
-* [`get_offdiagonal(::AbstractHamiltonian, address, chosen::Integer)`](@ref)
-* [`diagonal_element(::AbstractHamiltonian, address)`](@ref)
 * [`starting_address(::AbstractHamiltonian)`](@ref)
+* [`diagonal_element(::AbstractHamiltonian, address)`](@ref)
+* [`num_offdiagonals(::AbstractHamiltonian, address)`](@ref)
+* [`get_offdiagonal(::AbstractHamiltonian, address, chosen::Integer)`](@ref) (optional, see
+    below)
 
-Optional methods to implement:
+Optional additional methods to implement:
 
 * [`LOStructure(::Type{typeof(lo)})`](@ref LOStructure): defaults to `AdjointUnknown`
 * [`dimension(::AbstractHamiltonian, addr)`](@ref Main.Hamiltonians.dimension): defaults to
@@ -34,7 +35,7 @@ Optional methods to implement:
   `typeof(starting_address(h))`
 * [`momentum(::AbstractHamiltonian)`](@ref Main.Hamiltonians.momentum): no default
 
-Provides:
+Provides the following functions and methods:
 
 * [`offdiagonals`](@ref): iterator over reachable off-diagonal matrix elements
 * [`random_offdiagonal`](@ref): function to generate random off-diagonal matrix element
@@ -46,6 +47,11 @@ Provides:
 * [`BasisSetRep`](@ref Main.Hamiltonians.sparse): construct a basis set repesentation
 * [`sparse`](@ref Main.Hamiltonians.sparse), [`Matrix`](@ref): construct a (sparse) matrix representation
 
+Alternatively to the above, [`offdiagonals`](@ref) can be implemented instead of
+[`get_offdiagonal`](@ref). Sometimes this can be done efficiently. In this case
+[`num_offdiagonals`](@ref) should provide an upper bound on the number of elements obtained
+when iterating [`offdiagonals`](@ref).
+
 See also [`Hamiltonians`](@ref Main.Hamiltonians), [`Interfaces`](@ref).
 """
 abstract type AbstractHamiltonian{T} end
diff --git a/test/Hamiltonians.jl b/test/Hamiltonians.jl
index 0e4c56956..495b61376 100644
--- a/test/Hamiltonians.jl
+++ b/test/Hamiltonians.jl
@@ -13,12 +13,11 @@ function exact_energy(ham)
 end
 
 """
-    test_hamiltonian_interface(H, addr)
+    test_hamiltonian_interface(H, addr=starting_address(H))
 
 The main purpose of this test function is to check that all required methods are defined.
 """
-function test_hamiltonian_interface(H)
-    addr = starting_address(H)
+function test_hamiltonian_interface(H, addr=starting_address(H))
     @testset "$(nameof(typeof(H)))" begin
         @testset "*, mul!, and call" begin
             v = DVec(addr => eltype(H)(2.0))
@@ -59,11 +58,23 @@ function test_hamiltonian_interface(H)
             end
         end
         @testset "dimension" begin
-            @test dimension(H) ≥ dimension(H, starting_address(H))
+            @test dimension(H) == dimension(H, starting_address(H))
+            @test dimension(addr) ≥ dimension(H, addr)
         end
         @testset "allowed_address_type" begin
+            @test starting_address(H) isa allowed_address_type(H)
             @test addr isa allowed_address_type(H)
         end
+        @testset "offdiagonals" begin
+            # `get_offdiagonal` is not mandatory but `offdiagonals` is
+            if length(methods(get_offdiagonal, (typeof(H), typeof(add), Int))) > 0
+                ods = [get_offdiagonal(H, addr, i) for i in 1:num_offdiagonals(H, addr)]
+                @test ods == offdiagonals(H, addr)
+            end
+            number_of_nonzero_offdiagonals = length(DVec(offdiagonals(H, addr)))
+            @test number_of_nonzero_offdiagonals ≤ num_offdiagonals(H, addr)
+            @test number_of_nonzero_offdiagonals ≤ dimension(H, addr)
+        end
     end
 end
 
@@ -139,6 +150,7 @@ end
         HubbardReal1D(BoseFS((1, 2, 3, 4)); u=1.0, t=2.0),
         HubbardReal1DEP(BoseFS((1, 2, 3, 4)); u=1.0, t=2.0, v_ho=3.0),
         HubbardMom1D(BoseFS((6, 0, 0, 4)); t=1.0, u=0.5),
+        HubbardMom1D(OccupationNumberFS(6, 0, 0, 4); t=1.0, u=0.5),
         HubbardMom1D(BoseFS((6, 0, 0, 4)); t=1.0, u=0.5 + im),
         ExtendedHubbardReal1D(BoseFS((1,0,0,0,1)); u=1.0, v=2.0, t=3.0),
         HubbardRealSpace(BoseFS((1, 2, 3)); u=[1], t=[3]),