diff --git a/Project.toml b/Project.toml
index 97dd3ae..978bd6d 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "MixedSubdivisions"
 uuid = "291d046c-3347-11e9-1e74-c3d251d406c6"
 authors = ["Sascha Timme <sascha.timme@gmail.com>"]
-version = "0.2.0"
+version = "0.3.0"
 
 [deps]
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
@@ -11,8 +11,8 @@ StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 
 [compat]
 MultivariatePolynomials = "^0.2.8"
-ProgressMeter = "^0.8, ^0.9"
-StaticArrays = "^0.10"
+ProgressMeter = "^0.8, ^0.9, ^1.0"
+StaticArrays = "^0.9, ^0.10, ^0.11"
 
 [extras]
 PolynomialTestSystems = "4c526841-e1e8-562c-bfa9-9f39d642e243"
diff --git a/codecov.yml b/codecov.yml
new file mode 100644
index 0000000..db24720
--- /dev/null
+++ b/codecov.yml
@@ -0,0 +1 @@
+comment: off
diff --git a/docs/src/index.md b/docs/src/index.md
index c3cadb9..26fb703 100644
--- a/docs/src/index.md
+++ b/docs/src/index.md
@@ -127,5 +127,6 @@ normal
 indices
 MixedCellIterator
 mixed_cells
+fine_mixed_cells
 support
 ```
diff --git a/src/MixedSubdivisions.jl b/src/MixedSubdivisions.jl
index 088387c..5a5ddec 100644
--- a/src/MixedSubdivisions.jl
+++ b/src/MixedSubdivisions.jl
@@ -1520,7 +1520,8 @@ end
 
 Compute all (fine) mixed cells of the given `support` induced
 by a generic lifting. This guarantees that all induce intial forms binomials.
-Returns a `Vector` of all mixed cells and the corresponding lifting.
+Returns a `Vector` of all mixed cells and the corresponding lifting or `nothing` if the algorithm
+wasn't able to compute fine mixed cells. This can happen due to some current technical limitations.
 """
 function fine_mixed_cells(f::Vector{<:MP.AbstractPolynomialLike}, lifting_sampler=gaussian_lifting_sampler; show_progress=true)
     fine_mixed_cells(support(f), lifting_sampler)
@@ -1532,30 +1533,37 @@ function fine_mixed_cells(support::Vector{<:Matrix}, lifting_sampler=gaussian_li
         p = nothing
     end
 
-
-    while true
-        lifting = map(A -> lifting_sampler(size(A,2))::Vector{Int32}, support)
-        iter = MixedCellIterator(support, lifting)
-
-        all_valid = true
-        cells = MixedCell[]
-        ncells = 0
-        mv = 0
-        for cell in iter
-            if !is_fully_mixed_cell(cell, support, lifting)
-                all_valid = false
-                break
+    try
+        while true
+            lifting = map(A -> lifting_sampler(size(A,2))::Vector{Int32}, support)
+            iter = MixedCellIterator(support, lifting)
+
+            all_valid = true
+            cells = MixedCell[]
+            ncells = 0
+            mv = 0
+            for cell in iter
+                if !is_fully_mixed_cell(cell, support, lifting)
+                    all_valid = false
+                    break
+                end
+                ncells += 1
+                mv += cell.volume
+                push!(cells, copy(cell))
+                if p !== nothing
+                    ProgressMeter.update!(p, ncells; showvalues=((:mixed_volume, mv),))
+                end
             end
-            ncells += 1
-            mv += cell.volume
-            push!(cells, copy(cell))
-            if p !== nothing
-                ProgressMeter.update!(p, ncells; showvalues=((:mixed_volume, mv),))
+            if all_valid
+                p !== nothing && ProgressMeter.finish!(p; showvalues=((:mixed_volume, mv),))
+                return cells, lifting
             end
         end
-        if all_valid
-            p !== nothing && ProgressMeter.finish!(p; showvalues=((:mixed_volume, mv),))
-            return cells, lifting
+    catch e
+        if isa(e, InexactError) || isa(e, SingularException)
+            return nothing
+        else
+            rethrow(e)
         end
     end
 end