diff --git a/src/deprecated.jl b/src/deprecated.jl
index a6fdbc4c5..c22d6ab44 100644
--- a/src/deprecated.jl
+++ b/src/deprecated.jl
@@ -240,6 +240,11 @@ import Base: @deprecate
     (flag, stat) = Iprobe(src, tag, comm)
     flag || return (false, nothing, nothing)
     count = Get_count(stat, UInt8)
+    if isnothing(count)
+        # As in `recv`: counting in `UInt8` can only fail by overflowing the
+        # `Cint` that `MPI_Get_count` reports through.
+        error("`MPI.irecv`: the message is larger than $(typemax(Cint)) bytes, which `MPI_Get_count` cannot report")
+    end
     buf = Array{UInt8}(undef, count)
     stat = Recv!(buf, Get_source(stat), Get_tag(stat), comm)
     (true, MPI.deserialize(buf), stat)
diff --git a/src/group.jl b/src/group.jl
index 9dae360ef..fef07139b 100644
--- a/src/group.jl
+++ b/src/group.jl
@@ -49,7 +49,8 @@ end
 
 The rank of the process in the particular group.
 
-Returns an integer in the range `0:MPI.Group_size()-1`.
+Returns an integer in the range `0:MPI.Group_size()-1`, or `nothing` if the calling process
+is not a member of `group`.
 
 # External links
 $(_doc_external("MPI_Group_rank"))
@@ -57,6 +58,9 @@ $(_doc_external("MPI_Group_rank"))
 function Group_rank(group::Group)
     rank = Ref{Cint}()
     API.MPI_Group_rank(group, rank)
+    # `MPI_UNDEFINED` is not a rank; return `nothing` rather than let the
+    # sentinel escape as an ordinary integer.
+    rank[] == API.MPI_UNDEFINED[] && return nothing
     Int(rank[])
 end
 
diff --git a/src/nonblocking.jl b/src/nonblocking.jl
index da19460f6..64bddd422 100644
--- a/src/nonblocking.jl
+++ b/src/nonblocking.jl
@@ -415,7 +415,9 @@ end
 
 The number of entries received. `T` should match the argument provided by the receive call that set the status variable.
 
-If the number of entries received exceeds the limits of the count parameter, then it returns `MPI_UNDEFINED`.
+Returns `nothing` if there is no meaningful count to report, which MPI signals as
+`MPI_UNDEFINED`: either the number of entries received exceeds the limits of the count
+parameter, or the number of bytes received is not a whole multiple of the size of `T`.
 
 # External links
 $(_doc_external("MPI_Get_count"))
@@ -423,6 +425,9 @@ $(_doc_external("MPI_Get_count"))
 function Get_count(stat::Status, datatype::Datatype)
     count = Ref{Cint}()
     API.MPI_Get_count(Ref(stat), datatype, count)
+    # `MPI_UNDEFINED` is not a count; return `nothing` rather than let the
+    # sentinel escape as an ordinary integer (as `Waitany` and friends do).
+    count[] == API.MPI_UNDEFINED[] && return nothing
     Int(count[])
 end
 Get_count(stat::Status, ::Type{T}) where {T} = Get_count(stat, Datatype(T))
diff --git a/src/pointtopoint.jl b/src/pointtopoint.jl
index 76712f656..110ac5f9f 100644
--- a/src/pointtopoint.jl
+++ b/src/pointtopoint.jl
@@ -169,6 +169,12 @@ recv(comm::Comm, status=nothing; source::Integer=API.MPI_ANY_SOURCE[], tag::Inte
 function recv(source::Integer, tag::Integer, comm::Comm, status::Union{Ref{Status}, Nothing})
     msg, stat = Mprobe(comm, Status; source=source, tag=tag)
     count = Get_count(stat, UInt8)
+    if isnothing(count)
+        # Counting in `UInt8` can only fail by overflowing the `Cint` that
+        # `MPI_Get_count` reports through; a byte count is necessarily a whole
+        # multiple of `sizeof(UInt8)`, so that cause cannot arise here.
+        error("`MPI.recv`: the message is larger than $(typemax(Cint)) bytes, which `MPI_Get_count` cannot report")
+    end
     buf = Array{UInt8}(undef, count)
     Mrecv!(buf, msg, status)
     return MPI.deserialize(buf)
diff --git a/test/test_group.jl b/test/test_group.jl
index 5f20729b1..0f024223c 100644
--- a/test/test_group.jl
+++ b/test/test_group.jl
@@ -19,6 +19,17 @@ grp5 = MPI.Group_excl(grp, Int32[0])
 grp6 = MPI.Group_incl(grp, Int32[0])
 @test MPI.Group_size(grp6) == 1
 
+# `Group_rank` must report a non-member as `nothing` rather than let MPI's
+# `MPI_UNDEFINED` sentinel escape as an ordinary integer.  Rank 0 is not a
+# member of grp5, and every other rank is not a member of grp6.
+if MPI.Comm_rank(comm) == 0
+    @test MPI.Group_rank(grp5) === nothing
+    @test MPI.Group_rank(grp6) == 0
+else
+    @test MPI.Group_rank(grp5) == MPI.Comm_rank(comm) - 1
+    @test MPI.Group_rank(grp6) === nothing
+end
+
 # Don't free the other groups
 MPI.free(grp)
 
diff --git a/test/test_sendrecv.jl b/test/test_sendrecv.jl
index d9cd3c51c..e7d70dac0 100644
--- a/test/test_sendrecv.jl
+++ b/test/test_sendrecv.jl
@@ -32,6 +32,18 @@ stats = MPI.Waitall(reqs, MPI.Status)
 @test MPI.Get_count(stats[2], Float64) == N
 @test recv_mesg == recv_mesg_expected
 
+# `Get_count` must report `MPI_UNDEFINED` as `nothing` rather than let the
+# sentinel escape as an ordinary integer.  The message is N Float64s, and that
+# many bytes is not a whole multiple of the size of a three-byte struct, so
+# there is no integral count to report.
+struct ThreeBytes
+    a::UInt8
+    b::UInt8
+    c::UInt8
+end
+@test sizeof(Float64) * N % sizeof(ThreeBytes) != 0   # the premise of the test below
+@test MPI.Get_count(stats[2], ThreeBytes) === nothing
+
 @test MPI.Testall(reqs)