diff --git a/lib/cusparse/conversions.jl b/lib/cusparse/conversions.jl
index fc1f2c75a3..e477e049d4 100644
--- a/lib/cusparse/conversions.jl
+++ b/lib/cusparse/conversions.jl
@@ -332,7 +332,7 @@ for elty in (:Float32, :Float64, :ComplexF32, :ComplexF64)
     @eval begin
         function CuSparseMatrixCSC{$elty}(csr::CuSparseMatrixCSR{$elty}; index::SparseChar='O', action::cusparseAction_t=CUSPARSE_ACTION_NUMERIC, algo::cusparseCsr2CscAlg_t=CUSPARSE_CSR2CSC_ALG1)
             m,n = size(csr)
-            colPtr = CUDA.zeros(Cint, n+1)
+            colPtr = (index == 'O') ? CUDA.ones(Cint, n+1) : CUDA.zeros(Cint, n+1)
             rowVal = CUDA.zeros(Cint, nnz(csr))
             nzVal = CUDA.zeros($elty, nnz(csr))
             function bufferSize()
@@ -352,7 +352,7 @@ for elty in (:Float32, :Float64, :ComplexF32, :ComplexF64)
 
         function CuSparseMatrixCSR{$elty}(csc::CuSparseMatrixCSC{$elty}; index::SparseChar='O', action::cusparseAction_t=CUSPARSE_ACTION_NUMERIC, algo::cusparseCsr2CscAlg_t=CUSPARSE_CSR2CSC_ALG1)
             m,n    = size(csc)
-            rowPtr = CUDA.zeros(Cint,m+1)
+            rowPtr = (index == 'O') ? CUDA.ones(Cint, m+1) : CUDA.zeros(Cint, m+1)
             colVal = CUDA.zeros(Cint,nnz(csc))
             nzVal  = CUDA.zeros($elty,nnz(csc))
             function bufferSize()
@@ -379,7 +379,7 @@ for (elty, welty) in ((:Float16, :Float32),
     @eval begin
         function CuSparseMatrixCSC{$elty}(csr::CuSparseMatrixCSR{$elty}; index::SparseChar='O', action::cusparseAction_t=CUSPARSE_ACTION_NUMERIC, algo::cusparseCsr2CscAlg_t=CUSPARSE_CSR2CSC_ALG1)
             m,n = size(csr)
-            colPtr = CUDA.zeros(Cint, n+1)
+            colPtr = (index == 'O') ? CUDA.ones(Cint, n+1) : CUDA.zeros(Cint, n+1)
             rowVal = CUDA.zeros(Cint, nnz(csr))
             nzVal = CUDA.zeros($elty, nnz(csr))
             if $elty == Float16 #broken for ComplexF16?
@@ -405,7 +405,7 @@ for (elty, welty) in ((:Float16, :Float32),
 
         function CuSparseMatrixCSR{$elty}(csc::CuSparseMatrixCSC{$elty}; index::SparseChar='O', action::cusparseAction_t=CUSPARSE_ACTION_NUMERIC, algo::cusparseCsr2CscAlg_t=CUSPARSE_CSR2CSC_ALG1)
             m,n    = size(csc)
-            rowPtr = CUDA.zeros(Cint,m+1)
+            rowPtr = (index == 'O') ? CUDA.ones(Cint, m+1) : CUDA.zeros(Cint, m+1)
             colVal = CUDA.zeros(Cint,nnz(csc))
             nzVal  = CUDA.zeros($elty,nnz(csc))
             if $elty == Float16 #broken for ComplexF16?
@@ -586,10 +586,10 @@ end
 ## CSR to COO and vice-versa
 
 function CuSparseMatrixCSR{Tv}(coo::CuSparseMatrixCOO{Tv}; index::SparseChar='O') where {Tv}
-    m,n = size(coo)
-    nnz(coo) == 0 && return CuSparseMatrixCSR{Tv}(CUDA.ones(Cint, m+1), coo.colInd, nonzeros(coo), size(coo))
+    m, n = size(coo)
+    csrRowPtr = (index == 'O') ? CUDA.ones(Cint, m + 1) : CUDA.zeros(Cint, m + 1)
+    nnz(coo) == 0 && return CuSparseMatrixCSR{Tv}(csrRowPtr, coo.colInd, nonzeros(coo), size(coo))
     coo = sort_coo(coo, 'R')
-    csrRowPtr = CuVector{Cint}(undef, m+1)
     cusparseXcoo2csr(handle(), coo.rowInd, nnz(coo), m, csrRowPtr, index)
     CuSparseMatrixCSR{Tv}(csrRowPtr, coo.colInd, nonzeros(coo), size(coo))
 end
@@ -605,10 +605,10 @@ end
 ### CSC to COO and viceversa
 
 function CuSparseMatrixCSC{Tv}(coo::CuSparseMatrixCOO{Tv}; index::SparseChar='O') where {Tv}
-    m,n = size(coo)
-    nnz(coo) == 0 && return CuSparseMatrixCSC{Tv}(CUDA.ones(Cint, n+1), coo.rowInd, nonzeros(coo), size(coo))
+    m, n = size(coo)
+    cscColPtr = (index == 'O') ? CUDA.ones(Cint, n + 1) : CUDA.zeros(Cint, n + 1)
+    nnz(coo) == 0 && return CuSparseMatrixCSC{Tv}(cscColPtr, coo.rowInd, nonzeros(coo), size(coo))
     coo = sort_coo(coo, 'C')
-    cscColPtr = CuVector{Cint}(undef, n+1)
     cusparseXcoo2csr(handle(), coo.colInd, nnz(coo), n, cscColPtr, index)
     CuSparseMatrixCSC{Tv}(cscColPtr, coo.rowInd, nonzeros(coo), size(coo))
 end
diff --git a/test/libraries/cusparse/conversions.jl b/test/libraries/cusparse/conversions.jl
index 870d591fa0..f946fd1967 100644
--- a/test/libraries/cusparse/conversions.jl
+++ b/test/libraries/cusparse/conversions.jl
@@ -113,17 +113,19 @@ if !(v"12.0" <= CUSPARSE.version() < v"12.1")
     end
 end
 
-for (n, bd, p) in [(100, 5, 0.02), (5, 1, 0.8), (4, 2, 0.5)]
+for (n, bd, p) in [(100, 5, 0.02), (5, 1, 0.8), (4, 2, 0.5), (0, 1, 0.0)]
     v"12.0" <= CUSPARSE.version() < v"12.1" && n == 4 && continue
     @testset "conversions between CuSparseMatrices (n, bd, p) = ($n, $bd, $p)" begin
         A = sprand(n, n, p)
         blockdim = bd
         for CuSparseMatrixType1 in (CuSparseMatrixCSC, CuSparseMatrixCSR, CuSparseMatrixCOO, CuSparseMatrixBSR)
+            if CuSparseMatrixType1 == CuSparseMatrixBSR && n == 0 continue end # TODO: conversion to CuSparseMatrixBSR breaks with (0x0) matrices
             dA1 = CuSparseMatrixType1 == CuSparseMatrixBSR ? CuSparseMatrixType1(A, blockdim) : CuSparseMatrixType1(A)
             @testset "conversion $CuSparseMatrixType1 --> SparseMatrixCSC" begin
                 @test SparseMatrixCSC(dA1) ≈ A
             end
             for CuSparseMatrixType2 in (CuSparseMatrixCSC, CuSparseMatrixCSR, CuSparseMatrixCOO, CuSparseMatrixBSR)
+                if CuSparseMatrixType2 == CuSparseMatrixBSR && n == 0 continue end # TODO: conversion to CuSparseMatrixBSR breaks with (0x0) matrices
                 CuSparseMatrixType1 == CuSparseMatrixType2 && continue
                 dA2 = CuSparseMatrixType2 == CuSparseMatrixBSR ? CuSparseMatrixType2(dA1, blockdim) : CuSparseMatrixType2(dA1)
                 @testset "conversion $CuSparseMatrixType1 --> $CuSparseMatrixType2" begin