diff --git a/src/AbsSeries.jl b/src/AbsSeries.jl
index 8a25508a2..395a4a8a7 100644
--- a/src/AbsSeries.jl
+++ b/src/AbsSeries.jl
@@ -81,6 +81,13 @@ function Base.hash(a::AbsPowerSeriesRingElem, h::UInt)
    return b
 end
 
+function set_precision!(a::AbsPowerSeriesRingElem, prec::Int)
+   prec < 0 && throw(DomainError(prec, "Precision must be non-negative"))
+   a = truncate!(a, prec)
+   _set_precision_raw!(a, prec)
+   return a
+end
+
 ###############################################################################
 #
 #   Similar and zero
@@ -405,22 +412,7 @@ end
 Return $a$ truncated to $n$ terms.
 """
 function truncate(a::AbsPowerSeriesRingElem{T}, n::Int) where T <: RingElement
-   n < 0 && throw(DomainError(n, "n must be >= 0"))
-   len = length(a)
-   if precision(a) <= n
-      return a
-   end
-   z = parent(a)()
-   fit!(z, n)
-   z = _set_precision_raw!(z, n)
-   for i = 1:min(n, len)
-      z = setcoeff!(z, i - 1, coeff(a, i - 1))
-   end
-   for i = len + 1:n
-      z = setcoeff!(z, i - 1, zero(base_ring(a)))
-   end
-   z = set_length!(z, normalise(z, n))
-   return z
+   return truncate!(deepcopy(a), n)
 end
 
 ###############################################################################
diff --git a/src/RelSeries.jl b/src/RelSeries.jl
index 8a07f658c..04d1cde86 100644
--- a/src/RelSeries.jl
+++ b/src/RelSeries.jl
@@ -95,15 +95,14 @@ function set_length!(a::SeriesElem, len::Int)
    return a
 end
 
-# TODO: set_precision! for the generic types RelSeries and AbsSeries
-# truncates the underlying polynomial since #1773. In a breaking release,
-# this should possibly also happen for the abstract types. Alternatively,
-# this set_precision! should be renamed (and only be kept as a purely internal
-# setter function).
-function set_precision!(a::SeriesElem, prec::Int)
-  # TODO
-  _set_precision_raw!(a, prec)
-  return a
+function set_precision!(a::RelPowerSeriesRingElem, prec::Int)
+   prec < 0 && throw(DomainError(prec, "Precision must be non-negative"))
+   a = truncate!(a, prec)
+   _set_precision_raw!(a, prec)
+   if is_zero(a)
+      set_valuation!(a, prec)
+   end
+   return a
 end
 
 function _set_precision_raw!(a::SeriesElem, prec::Int)
@@ -581,27 +580,7 @@ end
 Return $a$ truncated to (absolute) precision $n$.
 """
 function truncate(a::RelPowerSeriesRingElem{T}, n::Int) where T <: RingElement
-   n < 0 && throw(DomainError(n, "n must be >= 0"))
-   alen = pol_length(a)
-   aprec = precision(a)
-   aval = valuation(a)
-   if aprec <= n
-      return a
-   end
-   z = parent(a)()
-   z = _set_precision_raw!(z, n)
-   if n <= aval
-      z = set_length!(z, 0)
-      z = set_valuation!(z, n)
-   else
-      fit!(z, n - aval)
-      z = set_valuation!(z, aval)
-      for i = 1:min(n - aval, alen)
-         z = setcoeff!(z, i - 1, polcoeff(a, i - 1))
-      end
-      z = set_length!(z, normalise(z, n - aval))
-   end
-   return z
+   return truncate!(deepcopy(a), n)
 end
 
 # Intended only for internal use, does not renormalize, assumes n >= 0
diff --git a/src/generic/AbsSeries.jl b/src/generic/AbsSeries.jl
index d81020e58..d12315ee8 100644
--- a/src/generic/AbsSeries.jl
+++ b/src/generic/AbsSeries.jl
@@ -72,13 +72,6 @@ function characteristic(a::AbsPowerSeriesRing{T}) where T <: RingElement
    return characteristic(base_ring(a))
 end
 
-function set_precision!(a::AbsSeries, prec::Int)
-   prec < 0 && throw(DomainError(prec, "Precision must be non-negative"))
-   a = truncate!(a, prec)
-   a.prec = prec
-   return a
-end
-
 ###############################################################################
 #
 #   Binary operations
diff --git a/src/generic/RelSeries.jl b/src/generic/RelSeries.jl
index 40bfda5fe..2acf06e9f 100644
--- a/src/generic/RelSeries.jl
+++ b/src/generic/RelSeries.jl
@@ -62,16 +62,6 @@ function characteristic(a::RelPowerSeriesRing{T}) where T <: RingElement
    return characteristic(base_ring(a))
 end
 
-function set_precision!(a::RelSeries, prec::Int)
-   prec < 0 && throw(DomainError(prec, "Precision must be non-negative"))
-   a = truncate!(a, prec)
-   a.prec = prec
-   if is_zero(a)
-      a.val = prec
-   end
-   return a
-end
-
 ###############################################################################
 #
 #   Binary operators
diff --git a/src/generic/exports.jl b/src/generic/exports.jl
index f5bf2a319..ce1aa4623 100644
--- a/src/generic/exports.jl
+++ b/src/generic/exports.jl
@@ -124,6 +124,7 @@ export to_univariate
 export total_degree
 export trailing_coefficient
 export truncate
+export truncate!
 export unit
 export universal_polynomial_ring
 export upscale