diff --git a/src/AbstractHyperrectangle.jl b/src/AbstractHyperrectangle.jl
index 8e1881fb75..d9de15faa0 100644
--- a/src/AbstractHyperrectangle.jl
+++ b/src/AbstractHyperrectangle.jl
@@ -58,39 +58,36 @@ end
 # iterator that wraps the generator matrix
 struct HyperrectangleGeneratorIterator{AH<:AbstractHyperrectangle}
     H::AH
-    len::Int
+    nonflats::Vector{Int}  # dimensions along which `H` is not flat
+    dim::Int  # total number of dimensions of `H` (stored for efficiency)
 
     function HyperrectangleGeneratorIterator(H::AH) where {N<:Real,
             AH<:AbstractHyperrectangle{N}}
-        len = dim(H)
-        for i in 1:len
-            if radius_hyperrectangle(H, i) == zero(N)
-                len -= 1
+        n = dim(H)
+        nonflats = Vector{Int}()
+        sizehint!(nonflats, n)
+        @inbounds for i in 1:n
+            if radius_hyperrectangle(H, i) != zero(N)
+                push(nonflats, i)
             end
         end
-        return new{AH}(H, len)
+        return new{AH}(H, nonflats, n)
     end
 end
 
-Base.length(it::HyperrectangleGeneratorIterator) = it.len
+Base.length(it::HyperrectangleGeneratorIterator) = length(it.nonflats)
 
 Base.eltype(::Type{<:HyperrectangleGeneratorIterator{<:AbstractHyperrectangle{N}}}) where {N} =
     Approximations.UnitVector{N}
 
 function Base.iterate(it::HyperrectangleGeneratorIterator{<:AH},
                       state::Int=1) where {N, AH<:AbstractHyperrectangle{N}}
-    local r
-    while true
-        if state > dim(it.H)
-            return nothing
-        end
-        r = radius_hyperrectangle(it.H, state)
-        if r != zero(N)
-            break
-        end
-        state += 1
+    if state > length(it.nonflats)
+        return nothing
     end
-    g = Approximations.UnitVector(state, dim(it.H), r)
+    i = it.nonflats[state]
+    r = radius_hyperrectangle(it.H, i)
+    g = Approximations.UnitVector(i, it.dim, r)
     state += 1
     return (g, state)
 end
@@ -98,7 +95,7 @@ end
 """
     generators(H::AbstractHyperrectangle)
 
-Return an iterator over the (single) generator of a hyperrectangular set.
+Return an iterator over the generators of a hyperrectangular set.
 
 ### Input